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Dissertations / Theses on the topic 'Matrix methods'
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Ramachandran, Karuna. "Matrix geometric methods in priority queues." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq28517.pdf.
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Parambath, Shameem Ahamed Puthiya. "Matrix Factorization Methods for Recommender Systems." Thesis, Umeå universitet, Institutionen för datavetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-74181.
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This thesis is a comprehensive study of matrix factorization methods used in recommender systems. We study and analyze the existing models, specifically probabilistic models used in conjunction with matrix factorization methods, for recommender systems from a machine learning perspective. We implement two different methods suggested in scientific literature and conduct experiments on the prediction accuracy of the models on the Yahoo! Movies rating dataset.
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Kressner, Daniel. "Numerical Methods for Structured Matrix Factorizations." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10047770.
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Bright, Leslie William. "Matrix-analytic methods in applied probability /." Title page, table of contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phb855.pdf.
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CATALANO, COSTANZA. "Probabilisticts methods for primitive matrix semigroups." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9726.
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We study the primitivity property of finitely generated matrix semigroups from a probabilistic point of view and via two approaches. A finite set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive; the length of the shortest of these products is called the exponent of the set.
We firstly study the primitivity property of random matrix sets, by rephrasing it in terms of random labeled directed multigraphs. We extend classical models of random graph theory to labeled directed multigraphs and we show that these random models admit a sharp threshold with respect to the primitivity property. We also show that when primitive, these models have low exponent with high probability. We then prove that they exhibit the same threshold behavior with respect to the property of being column-primitive and we use these results for studying the 2-directability property and 3-directability property of random nondeterministic finite state automata (NDFAs). In particular, we show that an NDFA generated according to the uniform distribution admits a short 2-directing word and a short 3-directing word with high probability. Inspired by the probabilistic method, we then present a more involved randomized construction that generates primitive sets with large exponent
with nonvanishing probability and we use our findings for exhibiting new families of synchronizing finite state automata with quadratic reset threshold.
Secondly, we embed the primitivity problem in a probabilistic game framework in order to study its properties. We develop a tool, that we call the synchronizing probability function for primitive sets of matrices, that captures the speed at which a primitive set reaches its first positive product thus representing the convergence of the primitivity process, and we show that this function must increase regularly in some sense. We then show that this function can be used for efficiently approximating the exponent of any given primitive set made of matrices having neither zero-rows nor zero-columns (NZ-matrices) and for (potentially) improving the upper bound on the maximal exponent among the primitive sets of NZ-matrices. Finally, we prove that in a primitive semigroup
of matrix size n × n, for all k ≤ √n the length of the shortest product having a row or a column with k positive entries is linear in n, question that is still open for synchronizing automata.
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Terkhova, Karina. "Capacitance matrix preconditioning." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244593.
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Manukyan, Narine. "Improved Methods for Cluster Identification and Visualization." ScholarWorks @ UVM, 2011. http://scholarworks.uvm.edu/graddis/147.
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Self-organizing maps (SOMs) are self-organized projections of high dimensional data onto a low, typically two dimensional (2D), map wherein vector similarity is implicitly translated into topological closeness in the 2D projection. They are thus used for clustering and visualization of high dimensional data. However it is often challenging to interpret the results due to drawbacks of currently used methods for identifying and visualizing cluster boundaries in the resulting feature maps. In this thesis we introduce a new phase to the SOM that we refer to as the Cluster Reinforcement (CR) phase. The CR phase amplifies within-cluster similarity with the consequence that cluster boundaries become much more evident. We also define a new Boundary (B) matrix that makes cluster boundaries easy to visualize, can be thresholded at various levels to make cluster hierarchies apparent, and can be overlain directly onto maps of component planes (something that was not possible with previous methods). The combination of the SOM, CR phase and B-matrix comprise an automated method for improved identification and informative visualization of clusters in high dimensional data. We demonstrate these methods on three data sets: the classic 13- dimensional binary-valued “animal” benchmark test, actual 60-dimensional binaryvalued phonetic word clustering problem, and 3-dimensional real-valued geographic data clustering related to fuel efficiency of vehicle choice.
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Lamond, Bernard Fernand. "Matrix methods in queueing and dynamic programming." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/27124.
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We investigate some modern matrix methods for the solution of finite state stochastic models with an infinite time horizon. Markov and semi-Markov decision processes and finite queues in tandem with exponential service times are considered. The methods are based on the Drazin generalized inverse and use matrix decomposition.
Unlike the related Jordan canonical form, the decompositions considered are numerically tractable and use real arithmetic when the original matrix has real entries. The spectral structure of the transition matrix of a Markov chain, deduced from non-negative matrix theory, provides a decomposition from which the limiting and deviation matrices are directly obtained.
The matrix decomposition approach to the solution of Markov reward processes provides a new, simple derivation of the Laurent expansion of the resolvent. Many other basic results of dynamic programming are easily derived in a similar fashion and the extension to semi-Markov decision processes is straightforward. Further, numerical algorithms for matrix decomposition can be used efficiently in the policy iteration method, for evaluating the terms of the Laurent series.
The problem of finding the stationary distribution of a system with two finite queues in tandem, when the service times have an exponential distribution, can also be expressed in matrix form. Two numerical methods, one iterative and one using matrix decomposition, are reviewed for computing the stationary probabilities. Job-local-balance is used to derive some bounds on the call congestion. A numerical investigation of the bounds is included. It suggests that the bounds are insensitive to the distribution of the service times.Business, Sauder School of
Graduate
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Haider, Shahid Abbas. "Systolic arrays for the matrix iterative methods." Thesis, Loughborough University, 1993. https://dspace.lboro.ac.uk/2134/28173.
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The systolic array research was pioneered by H. T. Kung and C. E. Leiserson. Systolic arrays are special purpose synchronous architectures consisting of simple, regular and modular processors which are regularly interconnected to form an array. Systolic arrays are well suited for computational bound problems in Linear Algebra. In this thesis, the numerical problems, especially iterative algorithms are chosen and implemented on the linear systolic array. same.
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Roberts, Jeremy Alyn. "Advanced response matrix methods for full core analysis." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/87490.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 195-200).
Modeling full reactor cores with high fidelity transport methods is a difficult task, requiring the largest computers available today. This thesis presents work on an alternative approach using the eigenvalue response matrix method (ERMM). The basic idea of ERMM is to decompose a reactor spatially into local "nodes." Each node represents an independent fixed source transport problem, and the nodes are linked via approximate boundary conditions to reconstruct the global problem using potentially many fewer explicit unknowns than a direct fine mesh solution. This thesis addresses several outstanding issues related to the ERMM based on deterministic transport. In particular, advanced transport solvers were studied for application to the relatively small and frequently repeated problems characteristic of response function generation. This includes development of preconditioners based on diffusion for use in multigroup Krylov linear solvers. These new solver combinations are up to an order of magnitude faster than competing algorithms. Additionally, orthogonal bases for space, angle, and energy variables were investigated. For the spatial variable, a new basis set that incorporates a shape function characteristic of pin assemblies was found to reduce significantly the error in representing boundary currents. For the angular variable, it was shown that bases that conserve the partial current at a boundary perform very well, particularly for low orders. For the deterministic transport used in this work, such bases require use of specialized angular quadratures. In the energy variable, it was found that an orthogonal basis constructed using a representative energy spectrum provides an accurate alternative to few group calculations. Finally, a parallel ERMM code Serment was developed, incorporating the transport and basis development along with several new algorithms for solving the response matrix equations, including variants of Picard iteration, Steffensen's method, and Newton's method. Based on results from several benchmark models, it was found that an accelerated Picard iteration provides the best performance, but Newton's method may be more robust. Furthermore, initial scoping studies demonstrated good scaling on an [omicron](100) processor machine.
by Jeremy Alyn Roberts.
Ph. D.
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Bai, Shuanghua. "Numerical methods for constrained Euclidean distance matrix optimization." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/401542/.
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This thesis is an accumulation of work regarding a class of constrained Euclidean Distance Matrix (EDM) based optimization models and corresponding numerical approaches. EDM-based optimization is powerful for processing distance information which appears in diverse applications arising from a wide range of fields, from which the motivation for this work comes. Those problems usually involve minimizing the error of distance measurements as well as satisfying some Euclidean distance constraints, which may present enormous challenge to the existing algorithms. In this thesis, we focus on problems with two different types of constraints. The first one consists of spherical constraints which comes from spherical data representation and the other one has a large number of bound constraints which comes from wireless sensor network localization. For spherical data representation, we reformulate the problem as an Euclidean dis-tance matrix optimization problem with a low rank constraint. We then propose an iterative algorithm that uses a quadratically convergent Newton-CG method at its each step. We study fundamental issues including constraint nondegeneracy and the nonsingularity of generalized Jacobian that ensure the quadratic convergence of the Newton method. We use some classic examples from the spherical multidimensional scaling to demonstrate the exibility of the algorithm in incorporating various constraints. For wireless sensor network localization, we set up a convex optimization model using EDM which integrates connectivity information as lower and upper bounds on the elements of EDM, resulting in an EDM-based localization scheme that possesses both effciency and robustness in dealing with flip ambiguity under the presence of high level of noises in distance measurements and irregular topology of the concerning network of moderate size. To localize a large-scale network effciently, we propose a patching-stitching localization scheme which divides the network into several sub-networks, localizes each sub-network separately and stitching all the sub-networks together to get the recovered network. Mechanism for separating the network is discussed. EDM-based optimization model can be extended to add more constraints, resulting in a exible localization scheme for various kinds of applications. Numerical results show that the proposed algorithm is promising.
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Jung, Ho-Won. "Direct sparse matrix methods for interior point algorithms." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185133.
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Recent advances in linear programming solution methodology have focused on interior point algorithms. These are powerful new methods, achieving significant reductions in computer time for large LPs and solving problems significantly larger than previously possible. This dissertation describes the implementation of interior point algorithms. It focuses on applications of direct sparse matrix methods to sparse symmetric positive definite systems of linear equations on scalar computers and vector supercomputers. The most computationally intensive step in each iteration of any interior point algorithm is the numerical factorization of a sparse symmetric positive definite matrix. In large problems or relatively dense problems, 80-90% or more of computational time is spent in this step. This study concentrates on solution methods for such linear systems. It is based on modifications and extensions of graph theory applied to sparse matrices. The row and column permutation of a sparse symmetric positive definite matrix dramatically affects the performance of solution algorithms. Various reordering methods are considered to find the best ordering for various numerical factorization methods and computer architectures. It is assumed that the reordering method will follow the fill-preserving rule, i.e., not allow additional fill-ins beyond that provided by the initial ordering. To follow this rule, a modular approach is used. In this approach, the matrix is first permuted by using any minimum degree heuristic, and then the permuted matrix is again reordered according to a specific reordering objective. Results of different reordering methods are described. There are several ways to compute the Cholesky factor of a symmetric positive definite matrix. A column Cholesky algorithm is a popular method for dense and sparse matrix factorization on serial and parallel computers. Applying this algorithm to a sparse matrix requires the use of sparse vector operations. Graph theory is applied to reduce sparse vector computations. A second and relatively new algorithm is the multifrontal algorithm. This method uses dense operations for sparse matrix computation at the expense of some data manipulation. The performance of the column Cholesky and multifrontal algorithms in the numerical factorization of a sparse symmetric positive definite matrix on an IBM 3090 vector supercomputer is described.
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Laeuchli, Jesse Harrison. "Methods for Estimating The Diagonal of Matrix Functions." W&M ScholarWorks, 2016. https://scholarworks.wm.edu/etd/1477067934.
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Many applications such as path integral evaluation in Lattice Quantum Chromodynamics (LQCD), variance estimation of least square solutions and spline ts, and centrality measures in network analysis, require computing the diagonal of a function of a matrix, Diag(f(A)) where A is sparse matrix, and f is some function. Unfortunately, when A is large, this can be computationally prohibitive. Because of this, many applications resort to Monte Carlo methods. However, Monte Carlo methods tend to converge slowly. One method for dealing with this shortcoming is probing. Probing assumes that nodes that have a large distance between them in the graph of A, have only a small weight connection in f(A). to determine the distances between nodes, probing forms Ak. Coloring the graph of this matrix will group nodes that have a high distance between them together, and thus a small connection in f(A). This enables the construction of certain vectors, called probing vectors, that can capture the diagonals of f(A). One drawback of probing is in many cases it is too expensive to compute and store A^k for the k that adequately determines which nodes have a strong connection in f(A). Additionally, it is unlikely that the set of probing vectors required for A^k is a subset of the probing vectors needed for Ak+1. This means that if more accuracy in the estimation is required, all previously computed work must be discarded. In the case where the underlying problem arises from a discretization of a partial dierential equation (PDE) onto a lattice, we can make use of our knowledge of the geometry of the lattice to quickly create hierarchical colorings for the graph of A^k. A hierarchical coloring is one in which colors for A^{k+1} are created by splitting groups of nodes sharing a color in A^k. The hierarchical property ensures that the probing vectors used to estimate Diag(f(A)) are nested subsets, so if the results are inaccurate the estimate can be improved without discarding the previous work. If we do not have knowledge of the intrinsic geometry of the matrix, we propose two new classes of methods that improve on the results of probing. One method seeks to determine structural properties of the matrix f(A) by obtaining random samples of the columns of f(A). The other method leverages ideas arising from similar problems in graph partitioning, and makes use of the eigenvectors of f(A) to form effective hierarchical colorings. Our methods have thus far seen successful use in computational physics, where they have been applied to compute observables arising in LQCD. We hope that the renements presented in this work will enable interesting applications in many other elds.
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Boito, Paola. "Structured matrix based methods for approximate polynomial GCD." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85672.
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Rattana, Amornrat, and Christine Böckmann. "Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5927/.
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This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.
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Savas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.
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In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem, which is encountered in the field of state-space subspace system identification. More specifically the problem is \[ \min_{\rank(X) = k} \det (B - X A)(B - X A)\tp, \] where $A$ and $B$ are given matrices and we want to find $X$ under a certain rank condition that minimizes the determinant. This problem is not properly stated since it involves implicit assumptions on $A$ and $B$ so that $(B - X A)(B - X A)\tp$ is never singular. This deficiency of the determinant criterion is fixed by generalizing the minimization criterion to rank reduction and volume minimization of the objective matrix. The volume of a matrix is defined as the product of its nonzero singular values. We give an algorithm that solves the generalized problem and identify properties of the input and output signals causing a singular objective matrix. Classification problems occur in many applications. The task is to determine the label or class of an unknown object. The third paper concerns with classification of handwritten digits in the context of tensors or multidimensional data arrays. Tensor and multilinear algebra is an area that attracts more and more attention because of the multidimensional structure of the collected data in various applications. Two classification algorithms are given based on the higher order singular value decomposition (HOSVD). The main algorithm makes a data reduction using HOSVD of 98--99 \% prior the construction of the class models. The models are computed as a set of orthonormal bases spanning the dominant subspaces for the different classes. An unknown digit is expressed as a linear combination of the basis vectors. The resulting algorithm achieves 5\% in classification error with fairly low amount of computations. The remaining two papers discuss computational methods for the best multilinear rank approximation problem \[ \min_{\cB} \| \cA - \cB\| \] where $\cA$ is a given tensor and we seek the best low multilinear rank approximation tensor $\cB$. This is a generalization of the best low rank matrix approximation problem. It is well known that for matrices the solution is given by truncating the singular values in the singular value decomposition (SVD) of the matrix. But for tensors in general the truncated HOSVD does not give an optimal approximation. For example, a third order tensor $\cB \in \RR^{I \x J \x K}$ with rank$(\cB) = (r_1,r_2,r_3)$ can be written as the product \[ \cB = \tml{X,Y,Z}{\cC}, \qquad b_{ijk}=\sum_{\lambda,\mu,\nu} x_{i\lambda} y_{j\mu} z_{k\nu} c_{\lambda\mu\nu}, \] where $\cC \in \RR^{r_1 \x r_2 \x r_3}$ and $X \in \RR^{I \times r_1}$, $Y \in \RR^{J \times r_2}$, and $Z \in \RR^{K \times r_3}$ are matrices of full column rank. Since it is no restriction to assume that $X$, $Y$, and $Z$ have orthonormal columns and due to these constraints, the approximation problem can be considered as a nonlinear optimization problem defined on a product of Grassmann manifolds. We introduce novel techniques for multilinear algebraic manipulations enabling means for theoretical analysis and algorithmic implementation. These techniques are used to solve the approximation problem using Newton and Quasi-Newton methods specifically adapted to operate on products of Grassmann manifolds. The presented algorithms are suited for small, large and sparse problems and, when applied on difficult problems, they clearly outperform alternating least squares methods, which are standard in the field.
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Anderson, Penelope L. "Matrix based derivations and representations of Krylov subspace methods." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23766.
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This thesis is based on recent work by Paige which gave a formalism for presenting and analyzing the class of algorithms which manipulate an appropriate Krylov subspace in solving large sparse systems of linear equations. This formalism--a way of dividing a method of solution into a Krylov process and an associated subproblem--is described and then applied to several of the more popular algorithms in use today including the methods of Conjugate Gradients and BiConjugate Gradients. The aim is to clarify these algorithms to make them easier to understand, analyze and use. Several of the methods presented in this thesis were developed in exactly this way--notably the Symmetric LQ method and the Generalized Minimum Residual method--and required little or no effort to characterize using the formalism. It was successfully applied to Conjugate Gradients and BiConjugate Gradients, already recognized as being closely related to the symmetric and unsymmetric Lanczos processes respectively. The newer algorithms such as Conjugate Gradients Squared and BiConjugate Gradients Stabilized, with less obvious relation to a specific Krylov process, provided more difficulty in their clarification.
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Britnell, John R. "Cycle index methods for matrix groups over finite fields." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275602.
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Schutz, James Branch. "Test methods and analysis for glass-ceramic matrix composites." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13711.
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Lezar, Evan. "GPU acceleration of matrix-based methods in computational electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/6507.
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Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2011.ENGLISH ABSTRACT: This work considers the acceleration of matrix-based computational electromagnetic (CEM) techniques using graphics processing units (GPUs). These massively parallel processors have gained much support since late 2006, with software tools such as CUDA and OpenCL greatly simplifying the process of harnessing the computational power of these devices. As with any advances in computation, the use of these devices enables the modelling of more complex problems, which in turn should give rise to better solutions to a number of global challenges faced at present. For the purpose of this dissertation, CUDA is used in an investigation of the acceleration of two methods in CEM that are used to tackle a variety of problems. The first of these is the Method of Moments (MOM) which is typically used to model radiation and scattering problems, with the latter begin considered here. For the CUDA acceleration of the MOM presented here, the assembly and subsequent solution of the matrix equation associated with the method are considered. This is done for both single and double precision oating point matrices. For the solution of the matrix equation, general dense linear algebra techniques are used, which allow for the use of a vast expanse of existing knowledge on the subject. This also means that implementations developed here along with the results presented are immediately applicable to the same wide array of applications where these methods are employed. Both the assembly and solution of the matrix equation implementations presented result in signi cant speedups over multi-core CPU implementations, with speedups of up to 300x and 10x, respectively, being measured. The implementations presented also overcome one of the major limitations in the use of GPUs as accelerators (that of limited memory capacity) with problems up to 16 times larger than would normally be possible being solved. The second matrix-based technique considered is the Finite Element Method (FEM), which allows for the accurate modelling of complex geometric structures including non-uniform dielectric and magnetic properties of materials, and is particularly well suited to handling bounded structures such as waveguide. In this work the CUDA acceleration of the cutoff and dispersion analysis of three waveguide configurations is presented. The modelling of these problems using an open-source software package, FEniCS, is also discussed. Once again, the problem can be approached from a linear algebra perspective, with the formulation in this case resulting in a generalised eigenvalue (GEV) problem. For the problems considered, a total solution speedup of up to 7x is measured for the solution of the generalised eigenvalue problem, with up to 22x being attained for the solution of the standard eigenvalue problem that forms part of the GEV problem.
AFRIKAANSE OPSOMMING: In hierdie werkstuk word die versnelling van matriksmetodes in numeriese elektromagnetika (NEM) deur die gebruik van grafiese verwerkingseenhede (GVEe) oorweeg. Die gebruik van hierdie verwerkingseenhede is aansienlik vergemaklik in 2006 deur sagteware pakette soos CUDA en OpenCL. Hierdie toestelle, soos ander verbeterings in verwerkings vermoe, maak dit moontlik om meer komplekse probleme op te los. Hierdie stel wetenskaplikes weer in staat om globale uitdagings beter aan te pak. In hierdie proefskrif word CUDA gebruik om ondersoek in te stel na die versnelling van twee metodes in NEM, naamlik die Moment Metode (MOM) en die Eindige Element Metode (EEM). Die MOM word tipies gebruik om stralings- en weerkaatsingsprobleme op te los. Hier word slegs na die weerkaatsingsprobleme gekyk. CUDA word gebruik om die opstel van die MOM matriks en ook die daaropvolgende oplossing van die matriksvergelyking wat met die metode gepaard gaan te bespoedig. Algemene digte lineere algebra tegnieke word benut om die matriksvergelykings op te los. Dit stel die magdom bestaande kennis in die vagebied beskikbaar vir die oplossing, en gee ook aanleiding daartoe dat enige implementasies wat ontwikkel word en resultate wat verkry word ook betrekking het tot 'n wye verskeidenheid probleme wat die lineere algebra metodes gebruik. Daar is gevind dat beide die opstelling van die matriks en die oplossing van die matriksvergelyking aansienlik vinniger is as veelverwerker SVE implementasies. 'n Verselling van tot 300x en 10x onderkeidelik is gemeet vir die opstel en oplos fases. Die hoeveelheid geheue beskikbaar tot die GVE is een van die belangrike beperkinge vir die gebruik van GVEe vir groot probleme. Hierdie beperking word hierin oorkom en probleme wat selfs 16 keer groter is as die GVE se beskikbare geheue word geakkommodeer en suksesvol opgelos. Die Eindige Element Metode word op sy beurt gebruik om komplekse geometriee asook nieuniforme materiaaleienskappe te modelleer. Die EEM is ook baie geskik om begrensde strukture soos golfgeleiers te hanteer. Hier word CUDA gebruik of om die afsny- en dispersieanalise van drie gol eierkonfigurasies te versnel. Die implementasie van hierdie probleme word gedoen deur 'n versameling oopbronkode wat bekend staan as FEniCS, wat ook hierin bespreek word. Die probleme wat ontstaan in die EEM kan weereens vanaf 'n lineere algebra uitganspunt benader word. In hierdie geval lei die formulering tot 'n algemene eiewaardeprobleem. Vir die gol eier probleme wat ondersoek word is gevind dat die algemene eiewaardeprobleem met tot 7x versnel word. Die standaard eiewaardeprobleem wat 'n stap is in die oplossing van die algemene eiewaardeprobleem is met tot 22x versnel.
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Sundin, Martin. "Bayesian methods for sparse and low-rank matrix problems." Doctoral thesis, KTH, Signalbehandling, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-191139.
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Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information,it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type ofmodeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and estimates the non-zero components. By modeling the detection problem as an array processing problem and a Bayesian filtering problem, we improve the detection accuracy. Bayesian methods approximate the sparsity by probability distributions which are iteratively modified. We show one approach to making the Bayesian method the Relevance Vector Machine robust against sparse noise. Bayesian methods for low-rank matrix estimation typically use probability distributions which only depends on the singular values or a factorization approach. Here we introduce a new method, the Relevance Singular Vector Machine, which uses precision matrices with prior distributions to promote low-rank. The method is also applied to the robust Principal Component Analysis (PCA) problem, where a low-rank matrix is contaminated by sparse noise. In many estimation problems, there exists theoretical lower bounds on how well an algorithm can perform. When the performance of an algorithm matches a lowerbound, we know that the algorithm has optimal performance and that the lower bound is tight. When no algorithm matches a lower bound, there exists room for better algorithms and/or tighter bounds. In this thesis we derive lower bounds for three different Bayesian low-rank matrix models. In some problems, only the amplitudes of the measurements are recorded. Despitebeing non-linear, some problems can be transformed to linear problems. Earlier works have shown how sparsity can be utilized in the problem, here we show how the low-rank can be used. In some situations, the number of measurements and/or the number of parametersis very large. Such Big Data problems require us to design new algorithms. We show how the Basis Pursuit algorithm can be modified for problems with a very large number of parameters.Många vetenskapliga och ingenjörsproblem kräver att vi behandlar mätningar och data för att finna information. Eftersom vi grundar beslut på information är det viktigt att designa noggranna och effektiva behandlingsalgoritmer. Detta görs ofta genom att modellera signalen vi söker och bruset i problemet. En typ av modellering är Compressed Sensing där signalen har en gles eller lågrangs-representation.I denna avhandling studerar vi olika sätt att designa algoritmer för glesa och lågrangsproblem. Giriga metoder är snabba metoder för glesa problem som iterativt detekterar och skattar de nollskilda komponenterna. Genom att modellera detektionsproblemet som ett gruppantennproblem och ett Bayesianskt filtreringsproblem förbättrar vi prestandan hos algoritmerna. Bayesianska metoder approximerar glesheten med sannolikhetsfördelningar som iterativt modifieras. Vi visar ett sätt att göra den Bayesianska metoden Relevance Vector Machine robust mot glest brus. Bayesianska metoder för skattning av lågrangsmatriser använder typiskt sannolikhetsfördelningar som endast beror på matrisens singulärvärden eller en faktoriseringsmetod. Vi introducerar en ny metod, Relevance Singular Vector Machine, som använder precisionsmatriser med a-priori fördelningar för att införa låg rang. Metoden används också för robust Principal Komponent Analys (PCA), där en lågrangsmatris har störts av glest brus. I många skattningsproblem existerar det teoretiska undre gränser för hur väl en algoritm kan prestera. När en algoritm möter en undre gräns vet vi att algoritmen är optimal och att den undre gränsen är den bästa möjliga. När ingen algoritm möter en undre gräns vet vi att det existerar utrymme för bättre algoritmer och/eller bättre undre gränser. I denna avhandling härleder vi undre gränser för tre olika Bayesianska lågrangsmodeller. I vissa problem registreras endast amplituderna hos mätningarna. Några problem kan transformeras till linjära problem, trots att de är olinjära. Tidigare arbeten har visat hur gleshet kan användas i problemet, här visar vi hur låg rang kan användas. I vissa situationer är antalet mätningar och/eller antalet parametrar mycket stort. Sådana Big Data-problem kräver att vi designar nya algoritmer. Vi visar hur algoritmen Basis Pursuit kan modifieras när antalet parametrar är mycket stort.
QC 20160825
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Park, Joon-Soo. "Evaluation Methods for Fracture Resistance of Ceramic Matrix Composites." Kyoto University, 2003. http://hdl.handle.net/2433/148648.
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Kyoto University (京都大学)0048
新制・課程博士
博士(エネルギー科学)
甲第10330号
エネ博第66号
新制||エネ||20(附属図書館)
UT51-2003-H751
京都大学大学院エネルギー科学研究科エネルギー応用科学専攻
(主査)教授 香山 晃, 教授 石井 隆次, 教授 落合 庄治郎
学位規則第4条第1項該当
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Yang, Ning. "Structured matrix methods for computations on Bernstein basis polynomials." Thesis, University of Sheffield, 2013. http://etheses.whiterose.ac.uk/3311/.
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This thesis considers structure preserving matrix methods for computations on Bernstein polynomials whose coefficients are corrupted by noise. The ill-posed operations of greatest common divisor computations and polynomial division are considered, and it is shown that structure preserving matrix methods yield excellent results. With respect to greatest common divisor computations, the most difficult part is the computation of its degree, and several methods for its determination are presented. These are based on the Sylvester resultant matrix, and it is shown that a new form of the Sylvester resultant matrix in the modified Bernstein basis yields the best results. The B´ezout resultant matrix in the modified Bernstein basis is also considered, and it is shown that the results from it are inferior to those from the Sylvester resultant matrix in the modified Bernstein basis.
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Koikari, Souji. "Numerical Methods for Confluent Hypergeometric Function of Matrix Argument." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124531.
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Lawn, Jonathan Marcus. "Linear methods for camera motion recovery." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313704.
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Cotter, Nicholas Paul Kyle. "Scattering matrix modelling of optical gratings." Thesis, University of Exeter, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300552.
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Haber, René. "Transition Matrix Monte Carlo Methods for Density of States Prediction." Doctoral thesis, Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-146873.
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Ziel dieser Arbeit ist zunächst die Entwicklung einer Vergleichsgrundlage, auf Basis derer Algorithmen zur Berechnung der Zustandsdichte verglichen werden können. Darauf aufbauend wird ein bestehendes übergangsmatrixbasiertes Verfahren für das großkanonisch Ensemble um ein neues Auswerteverfahren erweitert. Dazu werden numerische Untersuchungen verschiedener Monte-Carlo-Algorithmen zur Berechnung der Zustandsdichte durchgeführt. Das Hauptaugenmerk liegt dabei auf Verfahren, die auf Übergangsmatrizen basieren, sowie auf dem Verfahren von Wang und Landau.
Im ersten Teil der Forschungsarbeit wird ein umfassender Überblick über Monte-Carlo-Methoden und Auswerteverfahren zur Bestimmung der Zustandsdichte sowie über verwandte Verfahren gegeben. Außerdem werden verschiedene Methoden zur Berechnung der Zustandsdichte aus Übergangsmatrizen vorgestellt und diskutiert.
Im zweiten Teil der Arbeit wird eine neue Vergleichsgrundlage für Algorithmen zur Bestimmung der Zustandsdichte erarbeitet. Dazu wird ein neues Modellsystem entwickelt, an dem verschiedene Parameter frei gewählt werden können und für das die exakte Zustandsdichte sowie die exakte Übergangsmatrix bekannt sind. Anschließend werden zwei weitere Systeme diskutiert für welche zumindest die exakte Zustandsdichte bekannt ist: das Ising Modell und das Lennard-Jones System.
Der dritte Teil der Arbeit beschäftigt sich mit numerischen Untersuchungen an einer Auswahl der vorgestellten Verfahren. Auf Basis der entwickelten Vergleichsgrundlage wird der Einfluss verschiedener Parameter auf die Qualität der berechneten Zustandsdichte quantitativ bestimmt. Es wird gezeigt, dass Übergangsmatrizen in Simulationen mit Wang-Landau-Verfahren eine wesentlich bessere Zustandsdichte liefern als das Verfahren selbst.
Anschließend werden die gewonnenen Erkenntnisse genutzt um ein neues Verfahren zu entwickeln mit welchem die Zustandsdichte mittels Minimierung der Abweichungen des detaillierten Gleichgewichts aus großen, dünnbesetzten Übergangsmatrizen gewonnen werden kann. Im Anschluss wird ein Lennard-Jones-System im großkanonischen Ensemble untersucht. Es wird gezeigt, dass durch das neue Verfahren Zustandsdichte und Dampfdruckkurve bestimmt werden können, welche qualitativ mit Referenzdaten übereinstimmen.
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Tvedt, Janet Elaine 1963. "Matrix representations and analytical solution methods for stochastic activity networks." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/278660.
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Stochastic activity networks, a probabilistic extension of Petri nets, can be used to evaluate the performance, dependability, and performability of a wide variety of systems. When analytical solution methods are used, it is necessary to generate a state-level representation of a model prior to solution. The transition-rate matrices obtained from this representation tend to be very large and sparse. Analytical solutions to such problems can only be obtained by exploiting the matrix sparsity both in storage and computation. We do this, by studying alternative matrix representation schemes and steady-state and transient solution methods, and implementing methods appropriate for problems of this type. The results suggest that the implemented techniques can yield analytical solutions for many realistic models of computer systems and networks. This is evidenced by the performance evaluation of a CSMA/CD Local area network.
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Shank, Stephen David. "Low-rank solution methods for large-scale linear matrix equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/273331.
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MathematicsPh.D.
We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations which may viewed as extensions of the classical Lyapunov and Sylvester equations. The first class of matrix equations that we consider are constrained Sylvester equations, which essentially consist of Sylvester's equation along with a constraint on the solution matrix. These therefore constitute a system of matrix equations. The second are generalized Lyapunov equations, which are Lyapunov equations with additional terms. Such equations arise as computational bottlenecks in model order reduction.
Temple University--Theses
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Cambareri, Valerio <1986>. "Matrix Designs and Methods for Secure and Efficient Compressed Sensing." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amsdottorato.unibo.it/6998/1/cambareri_valerio_phd_thesis.pdf.
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The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives.
Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware.
Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content.
Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.
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Cambareri, Valerio <1986>. "Matrix Designs and Methods for Secure and Efficient Compressed Sensing." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amsdottorato.unibo.it/6998/.
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The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives.
Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware.
Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content.
Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.
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Rubensson, Emanuel. "Sparse Matrices in Self-Consistent Field Methods." Licentiate thesis, Stockholm : KTH Biotechnology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4219.
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Killian, Tyler Norton Rao S. M. "Fast solution of large-body problems using domain decomposition and null-field generation in the method of moments." Auburn, Ala, 2009. http://hdl.handle.net/10415/1881.
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Sun, Xinyuan. "Kernel Methods for Collaborative Filtering." Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-theses/135.
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The goal of the thesis is to extend the kernel methods to matrix factorization(MF) for collaborative ltering(CF). In current literature, MF methods usually assume that the correlated data is distributed on a linear hyperplane, which is not always the case. The best known member of kernel methods is support vector machine (SVM) on linearly non-separable data. In this thesis, we apply kernel methods on MF, embedding the data into a possibly higher dimensional space and conduct factorization in that space. To improve kernelized matrix factorization, we apply multi-kernel learning methods to select optimal kernel functions from the candidates and introduce L2-norm regularization on the weight learning process. In our empirical study, we conduct experiments on three real-world datasets. The results suggest that the proposed method can improve the accuracy of the prediction surpassing state-of-art CF methods.
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Refsnæs, Runar Heggelien. "Matrix-Free Conjugate Gradient Methods for Finite Element Simulations on GPUs." Thesis, Norges Teknisk-Naturvitenskaplige Universitet, Institutt for fysikk, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10826.
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A block-structured approach for solving 2-dimensional finite element approximations of the Poisson equation on graphics processing units(GPUs) is developed. Linear triangular elements are used, and a matrix-free version of the conjugate gradient method is utilized for solving test problems with over 30 million elements. A speedup of 24 is achieved on a NVIDIA Tesla C1060 GPU when compared to a serial CPU version of the same solution approach, and a comparison is made with previous GPU implementations of the same problem.
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Kandiah, Vivek. "Application of the Google matrix methods for characterization of directed networks." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2434/.
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La théorie des réseaux complexes est un domaine récent et important de la recherche qui consiste étudier divers systèmes naturels ou artificiels d'un point de vue des graphes en considérant une collection d'objets interdépendants. Parmi les différents aspects de la théorie des réseaux complexes, cette thèse se concentre sur l'analyse des propriétés structurelles des réseaux dirigés. L'outil principal utilisé dans ce travail est la méthode de la matrice Google qui est une méthode dérivée de la théorie des chaînes de Markov. La construction de cette matrice et son lien avec les chaînes de Markov sont expliqués dans le second chapitre et les propriétés spectrales des valeurs propres y sont également discutées. L'accent est mis sur le vecteur propre principal dela matrice (le PageRank). La base du système de ranking donné par le Page Rank y est expliquée en détail et illustrée à travers plusieurs exemples dans les chapitres suivants. Les systèmes considérés ici sont: les séquences d'ADN de quelques espèces animales,le système nerveux du vers C. Elegans ainsi que l'antique jeu de stratégie sur plateau, le jeu de go. Dans le premier cas nous analysons les propriétés statistiques des chaînes symboliques sous le point de vue des réseaux dirigés et nous proposons une mesure simple de similarité entre les espèces basée sur le PageRank. Dans le second cas nous introduisons le concept du ranking complémentaire (le CheiRank) permettant de caractériser en deux dimensions les réseaux dirigés. Dans le troisième cas nous utilisons les vecteurs propres principaux pour mettre en évidence les coups importants joués lors d'une partie de Go et nous montrons que les vecteurs propres suivants peuvent contenir des informations de communautés de coups. Ces diverses applications montrent que l'information apportée par le PageRank peut s'avérer utile dans de nombreuses situations différentes affin d'obtenir un aperçu du problème sous un angle différent, qui est l'approche des réseaux dirigés, enrichissant ainsi notre compréhension des systèmes étudiésThe complex network theory is a recent field of great importance to study various systems under a graph perspective by considering a collection of interdependent objects. Among the different aspects of the complex networks, this thesis is focused on the analysis of structural properties of directed networks. The primary tool used in this work is the Google matrix method which is derived from the Markov chain theory. The construction of this matrix and its link with Markov chains are explored and the spectral properties of the eigenvalues are discussed with an emphasis on the dominant eigenvalue with its associated eigenvector(PageRank vector). The ranking system given by the PageRank is explained in detail and illustrated through several examples. The systems considered here are the DNA sequences of some animal species, the neural system of the C. Elegans worm and the ancient strategy board game : the game of Go. In the first case, the statistical properties of symbolic chains are analyzed through a directed network viewpoint and a similarity measure of species based on PageRank is proposed. In the second case, the complementary ranking system (CheiRank vector) is introduced to provide a two dimensional characterization of the directed networks. In the third case, the dominant eigenvectors are used to highlight the most important moves during a game of Go and it is shown that those eigenvectors contain more information than mere frequency counts of the moves. It is also discussed that eigenvectors other than the dominant ones might contain information about some community structures of moves. These applications show how the information brought by the PageRank can be useful in various situations to gain some interesting or original insight about the studied system and how it is helping to understand the organization of the underlying directed network
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POONDRU, SHIRDISH. "A NEW DIRECT MATRIX INVERSION METHOD FOR ECONOMICAL AND MEMORY EFFICIENT NUMERICAL SOLUTIONS." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060976742.
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Alexandersson, Per. "Combinatorial Methods in Complex Analysis." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-88808.
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The theme of this thesis is combinatorics, complex analysis and algebraic geometry. The thesis consists of six articles divided into four parts. Part A: Spectral properties of the Schrödinger equation This part consists of Papers I-II, where we study a univariate Schrödinger equation with a complex polynomial potential. We prove that the set of polynomial potentials that admit solutions to the Schrödingerequation is connected, under certain boundary conditions. We also study a similar result for even polynomial potentials, where a similar result is obtained. Part B: Graph monomials and sums of squares In this part, consisting of Paper III, we study natural bases for the space of homogeneous, symmetric and translation-invariant polynomials in terms of multigraphs. We find all multigraphs with at most six edges that give rise to non-negative polynomials, and which of these that can be expressed as a sum of squares. Such polynomials appear naturally in connection to expressing certain non-negative polynomials as sums of squares. Part C: Eigenvalue asymptotics of banded Toeplitz matrices This part consists of Papers IV-V. We give a new and generalized proof of a theorem by P. Schmidt and F. Spitzer concerning asymptotics of eigenvalues of Toeplitz matrices. We also generalize the notion of eigenvalues to rectangular matrices, and partially prove the a multivariate analogue of the above. Part D: Stretched Schur polynomials This part consists of Paper VI, where we give a combinatorial proof that certain sequences of skew Schur polynomials satisfy linear recurrences with polynomial coefficients.At the time of doctoral defence the following papers were unpublished and had a status as follows: Paper 5: Manuscript; Paper 6: Manuscript
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Mandula, Ondrej. "Super-resolution methods for fluorescence microscopy." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8909.
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Fluorescence microscopy is an important tool for biological research. However, the resolution of a standard fluorescence microscope is limited by diffraction, which makes it difficult to observe small details of a specimen’s structure. We have developed two fluorescence microscopy methods that achieve resolution beyond the classical diffraction limit. The first method represents an extension of localisation microscopy. We used nonnegative matrix factorisation (NMF) to model a noisy dataset of highly overlapping fluorophores with intermittent intensities. We can recover images of individual sources from the optimised model, despite their high mutual overlap in the original dataset. This allows us to consider blinking quantum dots as bright and stable fluorophores for localisation microscopy. Moreover, NMF allows recovery of sources each having a unique shape. Such a situation can arise, for example, when the sources are located in different focal planes, and NMF can potentially be used for three dimensional superresolution imaging. We discuss the practical aspects of applying NMF to real datasets, and show super-resolution images of biological samples labelled with quantum dots. It should be noted that this technique can be performed on any wide-field epifluorescence microscope equipped with a camera, which makes this super-resolution method very accessible to a wide scientific community. The second optical microscopy method we discuss in this thesis is a member of the growing family of structured illumination techniques. Our main goal is to apply structured illumination to thick fluorescent samples generating a large out-of-focus background. The out-of-focus fluorescence background degrades the illumination pattern, and the reconstructed images suffer from the influence of noise. We present a combination of structured illumination microscopy and line scanning. This technique reduces the out-of-focus fluorescence background, which improves the quality of the illumination pattern and therefore facilitates reconstruction. We present super-resolution, optically sectioned images of a thick fluorescent sample, revealing details of the specimen’s inner structure. In addition, in this thesis we also discuss a theoretical resolution limit for noisy and pixelated data. We correct a previously published expression for the so-called fundamental resolution measure (FREM) and derive FREM for two fluorophores with intermittent intensity. We show that the intensity intermittency of the sources (observed for quantum dots, for example) can increase the “resolution” defined in terms of FREM.
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Harbrecht, Helmut, and Reinhold Schneider. "Wavelet based fast solution of boundary integral equations." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600649.
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This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators which yields quasi-sparse system matrices. These matrices can be compressed such that the complexity for solving a boundary integral equation scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. Based on the wavelet Galerkin scheme we present also an adaptive algorithm. By numerical experiments we provide results which demonstrate the performance of our algorithm.
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Storkey, Amos James. "Efficient covariance matrix methods for Bayesian Gaussian processes and Hopfield neural networks." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313335.
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Ost, Alexander. "Performance of communication systems : a model-based approach with matrix-geometric methods /." New York : Springer, 2001. http://opac.nebis.ch/cgi-bin/showAbstract.pl?u20=354041438X.
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Fleming, Alan Ralph. "Matrix representations and methods in the analysis and design of digital circuits." Thesis, University of Hull, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306064.
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Bourne, Martin. "Structure-preserving matrix methods for computations on univariate and bivariate Bernstein polynomials." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/20860/.
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Curve and surface intersection finding is a fundamental problem in computer-aided geometric design (CAGD). This practical problem motivates the undertaken study into methods for computing the square-free factorisation of univariate and bivariate polynomials in Bernstein form. It will be shown how these two problems are intrinsically linked and how finding univariate polynomial roots and bivariate polynomial factors is equivalent to finding curve and surface intersection points. The multiplicities of a polynomial’s factors are maintained through the use of a square free factorisation algorithm and this is analogous to the maintenance of smooth intersections between curves and surfaces, an important property in curve and surface design. Several aspects of the univariate and bivariate polynomial factorisation problem will be considered. This thesis examines the structure of the greatest common divisor (GCD) problem within the context of the square-free factorisation problem. It is shown that an accurate approximation of the GCD can be computed from inexact polynomials even in the presence of significant levels of noise. Polynomial GCD computations are ill-posed, in that noise in the coefficients of two polynomials which have a common factor typically causes the polynomials to become coprime. Therefore, a method for determining the approximate greatest common divisor (AGCD) is developed, where the AGCD is defined to have the same degree as the GCD and its coefficients are sufficiently close to those of the exact GCD. The algorithms proposed assume no prior knowledge of the level of noise added to the exact polynomials, differentiating this method from others which require derived threshold values in the GCD computation. The methods of polynomial factorisation devised in this thesis utilise the Sylvester matrix and a sequence of subresultant matrices for the GCD finding component. The classical definition of the Sylvester matrix is extended to compute the GCD of two and three bivariate polynomials defined in Bernstein form, and a new method of GCD computation is devised specifically for bivariate polynomials in Bernstein form which have been defined over a rectangular domain. These extensions are necessary for the computation of the factorisation of bivariate polynomials defined in the Bernstein form.
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Ost, Alexander. "Performance of communication systems : a model based evaluation with matrix geometric methods /." Berlin ; Heidelberg [u.a.] : Springer, 2001. http://swbplus.bsz-bw.de/bsz090497023inh.htm.
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Thorndyke, Brian. "Quantum dynamics of finite atomic and molecular systems through density matrix methods." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0004287.
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Zivcovich, Franco. "Backward error accurate methods for computing the matrix exponential and its action." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/250078.
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The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.
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Zivcovich, Franco. "Backward error accurate methods for computing the matrix exponential and its action." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/250078.
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The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.
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郭騰川 and Tang-chuen Nick Kwok. "Dynamic stiffness method for curved structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31212359.
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Nehate, Girish. "Solving large scale support vector machine problems using matrix splitting and decomposition methods /." Search for this dissertation online, 2006. http://wwwlib.umi.com/cr/ksu/main.
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