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Literatura académica sobre el tema "Algebras, Linear Algorithms"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 1 de febrero de 2022

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Artículos de revistas sobre el tema "Algebras, Linear Algorithms"

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Chyzak, F., A. Quadrat y D. Robertz. "Effective algorithms for parametrizing linear control systems over Ore algebras". Applicable Algebra in Engineering, Communication and Computing 16, n.º 5 (noviembre de 2005): 319–76. http://dx.doi.org/10.1007/s00200-005-0188-6.

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Faybusovich, Leonid. "Linear systems in Jordan algebras and primal-dual interior-point algorithms". Journal of Computational and Applied Mathematics 86, n.º 1 (noviembre de 1997): 149–75. http://dx.doi.org/10.1016/s0377-0427(97)00153-2.

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Sayadi Shahraki, Marzieh, Maryam Zangiabadi y Hossein Mansouri. "A wide neighborhood predictor–corrector infeasible-interior-point method for Cartesian P∗(κ)-LCP over symmetric cones". Asian-European Journal of Mathematics 09, n.º 03 (2 de agosto de 2016): 1650049. http://dx.doi.org/10.1142/s1793557116500492.

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In this paper, we present a predictor–corrector infeasible-interior-point method based on a new wide neighborhood of the central path for linear complementarity problem over symmetric cones (SCLCP) with the Cartesian [Formula: see text]-property. The convergence of the algorithm is proved for commutative class of search directions. Moreover, using the theory of Euclidean Jordan algebras and some elegant tools, the iteration bound improves the earlier complexity of these kind of algorithms for the Cartesian [Formula: see text]-SCLCPs.

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Chyzak, F., A. Quadrat y D. Robertz. "Linear control systems over ore algebras: Effective algorithms for the computation of parametrizations". IFAC Proceedings Volumes 36, n.º 19 (septiembre de 2003): 147–54. http://dx.doi.org/10.1016/s1474-6670(17)33317-7.

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Wani Jamaludin, Irma Wani Jamaludin y Norhaliza Abdul Wahab. "Recursive Subspace Identification Algorithm using the Propagator Based Method". Indonesian Journal of Electrical Engineering and Computer Science 6, n.º 1 (1 de abril de 2017): 172. http://dx.doi.org/10.11591/ijeecs.v6.i1.pp172-179.

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<p>Subspace model identification (SMI) method is the effective method in identifying dynamic state space linear multivariable systems and it can be obtained directly from the input and output data. Basically, subspace identifications are based on algorithms from numerical algebras which are the QR decomposition and Singular Value Decomposition (SVD). In industrial applications, it is essential to have online recursive subspace algorithms for model identification where the parameters can vary in time. However, because of the SVD computational complexity that involved in the algorithm, the classical SMI algorithms are not suitable for online application. Hence, it is essential to discover the alternative algorithms in order to apply the concept of subspace identification recursively. In this paper, the recursive subspace identification algorithm based on the propagator method which avoids the SVD computation is proposed. The output from Numerical Subspace State Space System Identification (N4SID) and Multivariable Output Error State Space (MOESP) methods are also included in this paper.</p>

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JAMIOŁKOWSKI, ANDRZEJ. "ON APPLICATIONS OF PI-ALGEBRAS IN THE ANALYSIS OF QUANTUM CHANNELS". International Journal of Quantum Information 10, n.º 08 (diciembre de 2012): 1241007. http://dx.doi.org/10.1142/s0219749912410079.

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In this paper, we discuss some constructive procedures which can be used in characterizations of linear transformations which preserve the set of states of a fixed quantum system. Our methods are based on analyzing an explicit form of a linear positive map in its Kraus representation. In particular, we discuss the so-called partial commutativity of operators and its applications to investigation of decoherence-free subspaces. These subspaces can also be considered as a special class of quantum error correcting codes. Using the concept of standard polynomials and Amitsur–Levitzki theorem and other ideas from the so-called polynomial identity algebras (PI-algebras) we discuss some effective algorithms for analyzing properties of quantum channels.

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Bluman, G. W. y S. Kumei. "Symmetry-based algorithms to relate partial differential equations: I. Local symmetries". European Journal of Applied Mathematics 1, n.º 3 (septiembre de 1990): 189–216. http://dx.doi.org/10.1017/s0956792500000176.

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Simple and systematic algorithms for relating differential equations are given. They are based on comparing the local symmetries admitted by the equations. Comparisons of the infinitesimal generators and their Lie algebras of given and target equations lead to necessary conditions for the existence of mappings which relate them. Necessary and sufficient conditions are presented for the existence of invertible mappings from a given nonlinear system of partial differential equations to some linear system of equations with examples including the hodograph and Legendre transformations, and the linearizations of a nonlinear telegraph equation, a nonlinear diffusion equation, and nonlinear fluid flow equations. Necessary and sufficient conditions are also given for the existence of an invertible point transformation which maps a linear partial differential equation with variable coefficients to a linear equation with constant coefficients. Other types of mappings are also considered including the Miura transformation and the invertible mapping which relates the cylindrical KdV and the KdV equations.

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8

Chen, Chin Chun, Yuan Horng Lin, Jeng Ming Yih y Sue Fen Huang. "Construct Knowledge Structure of Linear Algebra". Advanced Materials Research 211-212 (febrero de 2011): 793–97. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.793.

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Apply interpretive structural modeling to construct knowledge structure of linear algebra. New fuzzy clustering algorithms improved fuzzy c-means algorithm based on Mahalanobis distance has better performance than fuzzy c-means algorithm. Each cluster of data can easily describe features of knowledge structures individually. The results show that there are six clusters and each cluster has its own cognitive characteristics. The methodology can improve knowledge management in classroom more feasible.

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Demmel, James, Ioana Dumitriu, Olga Holtz y Plamen Koev. "Accurate and efficient expression evaluation and linear algebra". Acta Numerica 17 (25 de abril de 2008): 87–145. http://dx.doi.org/10.1017/s0962492906350015.

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We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate’ we mean that the computed answer has relative error less than 1, i.e., has some correct leading digits. We also address efficiency, by which we mean algorithms that run in polynomial time in the size of the input. Our results will depend strongly on the model of arithmetic: most of our results will use the so-called traditional model (TM), where the computed result of op(a, b), a binary operation like a+b, is given by op(a, b) * (1+δ) where all we know is that |δ| ≤ ε ≪ 1. Here ε is a constant also known as machine epsilon.We will see a common reason for the following disparate problems to permit accurate and efficient algorithms using only the four basic arithmetic operations: finding the eigenvalues of a suitably discretized scalar elliptic PDE, finding eigenvalues of arbitrary products, inverses, or Schur complements of totally non-negative matrices (such as Cauchy and Vandermonde), and evaluating the Motzkin polynomial. Furthermore, in all these cases the high accuracy is ‘deserved’, i.e., the answer is determined much more accurately by the data than the conventional condition number would suggest.In contrast, we will see that evaluating even the simple polynomial x + y + z accurately is impossible in the TM, using only the basic arithmetic operations. We give a set of necessary and sufficient conditions to decide whether a high accuracy algorithm exists in the TM, and describe progress toward a decision procedure that will take any problem and provide either a high-accuracy algorithm or a proof that none exists.When no accurate algorithm exists in the TM, it is natural to extend the set of available accurate operations by a library of additional operations, such as x + y + z, dot products, or indeed any enumerable set which could then be used to build further accurate algorithms. We show how our accurate algorithms and decision procedure for finding them extend to this case.Finally, we address other models of arithmetic, and the relationship between (im)possibility in the TM and (in)efficient algorithms operating on numbers represented as bit strings.

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Fabregat-Traver, Diego y Paolo Bientinesi. "Application-tailored linear algebra algorithms". International Journal of High Performance Computing Applications 27, n.º 4 (18 de julio de 2013): 426–39. http://dx.doi.org/10.1177/1094342013494428.

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Tesis sobre el tema "Algebras, Linear Algorithms"

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Gunnels, John Andrew. "A systematic approach to the design and analysis of linear algebra algorithms". Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3037015.

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Porter, Annabelle Louise. "The evolution of equation-solving: Linear, quadratic, and cubic". CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3069.

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This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.

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Wu, Wenhao. "High-performance matrix multiplication hierarchical data structures, optimized kernel routines, and qualitative performance modeling /". Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-07092003-003633.

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Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear". Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.

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Doutoramento em Matemática
Nesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias são representadas pelas chamadas séries de Chen. Estuda-se a representação formal destas séries através da introdução de várias álgebras não associativas e técnicas específicas de álgebras de Lie livres. Sistemas de coordenadas para estes sistemas são estudados, nomeadamente, coordenadas de primeiro tipo e de segundo tipo. Apresenta-se uma demonstração alternativa para as coordenadas de segundo tipo e obtêm-se expressões explícitas para as coordenadas de primeiro tipo. Estas últimas estão intimamente ligadas ao logaritmo da série de Chen que, por sua vez, tem fortes relações com uma fórmula designada na literatura por “continuous Baker-Campbell- Hausdorff formula”. São ainda apresentadas aplicações à teoria de funções simétricas não comutativas. É, por fim, caracterizado o mapa de monodromia de um campo de vectores não linear e periódico no tempo em relação a uma truncatura do logaritmo de Chen. No segundo tópico é estudada a estabilizabilidade de um sistema de quaisquer dois corpos que rolem um sobre o outro sem deslizar ou torcer. Constroem-se controlos fechados e dependentes do tempo que tornam a origem do sistema de dois corpos num sistema localmente assimptoticamente estável. Vários exemplos e algumas implementações em Maple°c são discutidos. No terceiro tópico, em apêndice, constroem-se algoritmos para calcular o valor de várias funções fundamentais na aritmética digital, sendo possível a sua implementação em microprocessadores. São também obtidos os seus domínios de convergência. No último tópico, também em apêndice, demonstra-se a existência e unicidade de solução para uma classe de equações integrais não lineares com atraso. O atraso tem um carácter funcional, mostrando-se ainda a diferenciabilidade no sentido de Fréchet da solução em relação à função de atraso.
In this PhD thesis several subjects are studied regarding the following topics: formulas for nonlinear control systems on free Lie algebras, stabilizability of nonlinear control systems, digital arithmetic algorithms, and nonlinear Fredholm integral equations with delay. The first and principal topic is mainly related with a problem known as the continuous Baker-Campbell-Hausdorff exponents. We propose a calculus to deal with formal nonautonomous ordinary differential equations evolving on the algebra of formal series defined on an alphabet. We introduce and connect several (non)associative algebras as Lie, shuffle, zinbiel, pre-zinbiel, chronological (pre-Lie), pre-chronological, dendriform, D-I, and I-D. Most of those notions were also introduced into the universal enveloping algebra of a free Lie algebra. We study Chen series and iterated integrals by relating them with nonlinear control systems linear in control. At the heart of all the theory of Chen series resides a zinbiel and shuffle homomorphism that allows us to construct a purely formal representation of Chen series on algebras of words. It is also given a pre-zinbiel representation of the chronological exponential, introduced by A.Agrachev and R.Gamkrelidze on the context of a tool to deal with nonlinear nonautonomous ordinary differential equations over a manifold, the so-called chronological calculus. An extensive description of that calculus is made, collecting some fragmented results on several publications. It is a fundamental tool of study along the thesis. We also present an alternative demonstration of the result of H.Sussmann about coordinates of second kind using the mentioned tools. This simple and comprehensive proof shows that coordinates of second kind are exactly the image of elements of the dual basis of a Hall basis, under the above discussed homomorphism. We obtain explicit expressions for the logarithm of Chen series and the respective coordinates of first kind, by defining several operations on a forest of leaf-labelled trees. It is the same as saying that we have an explicit formula for the functional coefficients of the Lie brackets on a continuous Baker-Campbell-Hausdorff-Dynkin formula when a Hall basis is used. We apply those formulas to relate some noncommutative symmetric functions, and we also connect the monodromy map of a time-periodic nonlinear vector field with a truncation of the Chen logarithm. On the second topic, we study any system of two bodies rolling one over the other without twisting or slipping. By using the Chen logarithm expressions, the monodromy map of a flow and Lyapunov functions, we construct time-variant controls that turn the origin of a control system linear in control into a locally asymptotically stable equilibrium point. Stabilizers for control systems whose vector fields generate a nilpotent Lie algebra with degree of nilpotency · 3 are also given. Some examples are presented and Maple°c were implemented. The third topic, on appendix, concerns the construction of efficient algorithms for Digital Arithmetic, potentially for the implementation in microprocessors. The algorithms are intended for the computation of several functions as the division, square root, sines, cosines, exponential, logarithm, etc. By using redundant number representations and methods of Lyapunov stability for discrete dynamical systems, we obtain several algorithms (that can be glued together into an algorithm for parallel execution) having the same core and selection scheme in each iteration. We also prove their domains of convergence and discuss possible extensions. The last topic, also on appendix, studies the set of solutions of a class of nonlinear Fredholm integral equations with general delay. The delay is of functional character modelled by a continuous lag function. We ensure existence and uniqueness of a continuous (positive) solution of such equation. Moreover, under additional conditions, it is obtained the Fr´echet differentiability of the solution with respect to the lag function.

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Yelkenci, Serhat. "Algorithmic Music Composition Using Linear Algebra". Thesis, Southern Illinois University at Edwardsville, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10275073.

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Sound, in its all forms, is a source of energy whose capabilities humankind is not yet fully aware of. Composition - the way of aggregating sounds into the form of music - still holds to be an unperceived methodology with lots of unknowns. Methodologies used by composers are generally seem as being innate talent, something that cannot be used or shared by others. Yet, as any other form of art, music actually is and can be interpreted with mathematics and geometry. The focus of this thesis is to propose a generative algorithm to compose structured music pieces using linear algebra as the mathematical language for the representation of music. By implementing the linear algebra as the scientific framework, a practical data structure is obtained for analysis and manipulation. Instead of defining a single structure from a certain musical canon, which is a type of limiting the frame of music, the generative algorithm proposed in this paper is capable of learning all kinds of musical structures by linear algebra operations. The algorithm is designed to build musical knowledge (influence) by analyzing music pieces and receive a new melody as the inspirational component to produce new unique and meaningful music pieces. Characteristic analysis features obtained from analyzing music pieces, serves as constraints during the composition process. The proposed algorithm has been successful in generating unique and meaningful music pieces. The process time of the algorithm varies due to complexity of the influential aspect. Yet, the free nature of the generative algorithm and the capability of matrical representation offer a practical linkage between unique and meaningful music creation and any other concept containing a mathematical foundation.

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Delaplace, Claire. "Algorithmes d'algèbre linéaire pour la cryptographie". Thesis, Rennes 1, 2018. http://www.theses.fr/2018REN1S045/document.

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Dans cette thèse, nous discutons d’aspects algorithmiques de trois différents problèmes, en lien avec la cryptographie. La première partie est consacrée à l’algèbre linéaire creuse. Nous y présentons un nouvel algorithme de pivot de Gauss pour matrices creuses à coefficients exacts, ainsi qu’une nouvelle heuristique de sélection de pivots, qui rend l’entière procédure particulièrement efficace dans certains cas. La deuxième partie porte sur une variante du problème des anniversaires, avec trois listes. Ce problème, que nous appelons problème 3XOR, consiste intuitivement à trouver trois chaînes de caractères uniformément aléatoires de longueur fixée, telles que leur XOR soit la chaîne nulle. Nous discutons des considérations pratiques qui émanent de ce problème et proposons un nouvel algorithme plus rapide à la fois en théorie et en pratique que les précédents. La troisième partie est en lien avec le problème learning with errors (LWE). Ce problème est connu pour être l’un des principaux problèmes difficiles sur lesquels repose la cryptographie à base de réseaux euclidiens. Nous introduisons d’abord un générateur pseudo-aléatoire, basé sur la variante dé-randomisée learning with rounding de LWE, dont le temps d’évaluation est comparable avec celui d’AES. Dans un second temps, nous présentons une variante de LWE sur l’anneau des entiers. Nous montrerons que dans ce cas le problème est facile à résoudre et nous proposons une application intéressante en re-visitant une attaque par canaux auxiliaires contre le schéma de signature BLISS
In this thesis, we discuss algorithmic aspects of three different problems, related to cryptography. The first part is devoted to sparse linear algebra. We present a new Gaussian elimination algorithm for sparse matrices whose coefficients are exact, along with a new pivots selection heuristic, which make the whole procedure particularly efficient in some cases. The second part treats with a variant of the Birthday Problem with three lists. This problem, which we call 3XOR problem, intuitively consists in finding three uniformly random bit-strings of fixed length, such that their XOR is the zero string. We discuss practical considerations arising from this problem, and propose a new algorithm which is faster in theory as well as in practice than previous ones. The third part is related to the learning with errors (LWE) problem. This problem is known for being one of the main hard problems on which lattice-based cryptography relies. We first introduce a pseudorandom generator, based on the de-randomised learning with rounding variant of LWE, whose running time is competitive with AES. Second, we present a variant of LWE over the ring of integers. We show that in this case the problem is easier to solve, and we propose an interesting application, revisiting a side-channel attack against the BLISS signature scheme

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Weihrauch, Christian. "Analysis of Monte Carlo algorithms for linear algebra problems". Thesis, University of Reading, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.515747.

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Iakymchuk, Roman [Verfasser]. "Performance modeling and prediction for linear algebra algorithms / Roman Iakymchuk". Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1026308690/34.

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Sato, Hiroyuki. "Riemannian Optimization Algorithms and Their Applications to Numerical Linear Algebra". 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/180615.

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Maust, Reid S. "Optimal power flow using a genetic algorithm and linear algebra". Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=1163.

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Thesis (Ph. D.)--West Virginia University, 1999.
Title from document title page. Document formatted into pages; contains vi, 91 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 41-42).

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Libros sobre el tema "Algebras, Linear Algorithms"

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service), SpringerLink (Online, ed. Max-linear Systems: Theory and Algorithms. London: Springer-Verlag London Limited, 2010.

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Kepner, Jeremy V. Graph algorithms in the language of linear algebra. Philadelphia: Society for Industrial and Applied Mathematics, 2011.

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Mersini, Nexhat. Sparse matrices of high order: Algorythms for reordering, inversion and solution of systems of linear equations = Matrica te rralla te rendeve te larta : algoritme per aranzhimin, inversimin dhe zgjidhjen e sistemeve te ekuacioneve lineare. Tirane: VEFA, 1996.

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Van Landingham, Hugh F., 1935-, ed. Algorithms for computer-aided design of multivariable control systems. New York: M. Dekker, 1993.

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NATO, Advanced Study Institute on Linear Algebra Digital Signal Processing and Parallel Algorithms (1988 Leuven Belgium). Numerical linear algebra, digital signal processing, and parallel algorithms. Berlin: Springer-Verlag, 1991.

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Svetozar, Margenov, ed. Robust algebraic multilevel methods and algorithms. Berlin: Walter De Gruyter, 2009.

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NATO Advanced Study Institute on Computer Algorithms for Solving Linear Equations: the State of the Art (1990 Il Ciocco, Italy). Computer algorithms for solving linear algebraic equations: The state of the art. Berlin: Springer-Verlag, 1991.

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NATO Advanced Study Institute on Computer Algorithms for Solving Linear Equations: the State of the Art (1990 Il Ciocco, Italy). Computer algorithms for solving linear algebraic equations: The state of the art. Berlin: Springer-Verlag, 1991.

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Wrixon, Adrian. D-A converter test optimisation. Dublin: University College Dublin, 1996.

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service), SpringerLink (Online, ed. The Linear Algebra a Beginning Graduate Student Ought to Know. 3^a ed. Dordrecht: Springer Netherlands, 2012.

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Capítulos de libros sobre el tema "Algebras, Linear Algorithms"

1

Dostál, Zdenek. "Linear Algebra". En Optimal Quadratic Programming Algorithms, 1–24. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-84806-8_1.

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Dostál, Zdeněk y Tomáš Kozubek. "Linear Algebra". En Scalable Algorithms for Contact Problems, 11–27. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-6834-3_2.

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Oliveira, Carlos. "Linear Algebra Algorithms". En Options and Derivatives Programming in C++20, 213–40. Berkeley, CA: Apress, 2020. http://dx.doi.org/10.1007/978-1-4842-6315-0_9.

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Oliveira, Carlos. "Linear Algebra Algorithms". En Options and Derivatives Programming in C++, 143–60. Berkeley, CA: Apress, 2016. http://dx.doi.org/10.1007/978-1-4842-1814-3_9.

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Winkler, Franz. "Linear algebra—solving linear systems". En Polynomial Algorithms in Computer Algebra, 157–71. Vienna: Springer Vienna, 1996. http://dx.doi.org/10.1007/978-3-7091-6571-3_7.

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Poloni, Federico. "Linear algebra preliminaries". En Algorithms for Quadratic Matrix and Vector Equations, 1–11. Pisa: Scuola Normale Superiore, 2011. http://dx.doi.org/10.1007/978-88-7642-384-0_1.

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Barg, Alexander. "Minimun distance decoding algorithms for linear codes". En Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 1–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63163-1_1.

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Fripertinger, Harald y Adalbert Kerber. "Isometry classes of indecomposable linear codes". En Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 194–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60114-7_15.

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Greferath, M. y S. E. Schmidt. "Linear Codes and Rings of Matrices". En Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 160–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46796-3_16.

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Janiszczak, Ingo, Reinhard Knörr y Gerhard O. Michler. "Gauß’scher Algorithmus". En Lineare Algebra für Wirtschaftsinformatiker, 55–68. Wiesbaden: Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-322-84176-6_8.

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Actas de conferencias sobre el tema "Algebras, Linear Algorithms"

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Pernet, Clément. "Exact Linear Algebra Algorithmic". En ISSAC'15: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2755996.2756684.

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Hubay, Csanád Árpád y Tamás Kalmár-Nagy. "Computing Poincaré-Lyapunov Constants via Carleman Linearization". En ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98413.

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Abstract Using Carleman linearization an approximation is given for the solution of a system at Hopf bifurcation. The values of the Poincaré-Lyapunov constants (whether they are zero or not) affect the linear algebraic properties of the Carleman matrix and they appear in solvability conditions (through the Fredholm alternative). We provide a linear algebra based algorithm to compute the Poincaré-Lyapunov constants.

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"UNREVEALING BIOLOGICAL PROCESS WITH LINEAR ALGEBRA - Extracting Patterns from Noisy Data". En International Conference on Bioinformatics Models, Methods and Algorithms. SciTePress - Science and and Technology Publications, 2011. http://dx.doi.org/10.5220/0003164103130317.

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4

Zhang, Shaoshuai, Vivek Karihaloo y Panruo Wu. "Basic Linear Algebra Operations on TensorCore GPU". En 2020 IEEE/ACM 11th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA). IEEE, 2020. http://dx.doi.org/10.1109/scala51936.2020.00011.

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5

Cheung, Ho Yee, Lap Chi Lau y Kai Man Leung. "Algebraic Algorithms for Linear Matroid Parity Problems". En Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2011. http://dx.doi.org/10.1137/1.9781611973082.105.

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6

Davila, Diego, Vassil Alexandrov y Oscar A. Esquivel-Flores. "On Monte Carlo Hybrid Methods for Linear Algebra". En 2016 7th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA). IEEE, 2016. http://dx.doi.org/10.1109/scala.2016.015.

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Xu, Guanglei y William S. Oates. "Can Quantum Computers Solve Linear Algebra Problems to Advance Engineering Applications?" En ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/smasis2018-8087.

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Since its inception by Richard Feynman in 1982, quantum computing has provided an intriguing opportunity to advance computational capabilities over classical computing. Classical computers use bits to process information in terms of zeros and ones. Quantum computers use the complex world of quantum mechanics to carry out calculations using qubits (the quantum analog of a classical bit). The qubit can be in a superposition of the zero and one state simultaneously unlike a classical bit. The true power of quantum computing comes from the complexity of entanglement between many qubits. When entanglement is realized, quantum algorithms for problems such as factoring numbers and solving linear algebra problems show exponential speed-up relative to any known classical algorithm. Linear algebra problems are of particular interest in engineering application for solving problems that use finite element and finite difference methods. Here, we explore quantum linear algebra problems where we design and implement a quantum circuit that can be tested on IBM’s quantum computing hardware. A set of quantum gates are assimilated into a circuit and implemented on the IBM Q system to demonstrate its algorithm capabilities and its measurement methodology.

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8

Eijkhout, Victor y Erika Fuentes. "Multi-stage Learning of Linear Algebra Algorithms". En 2008 Seventh International Conference on Machine Learning and Applications. IEEE, 2008. http://dx.doi.org/10.1109/icmla.2008.10.

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9

Casasent, David. "Optical Linear Algebra Processors: Architectures and Algorithms". En O-E/LASE'86 Symp (January 1986, Los Angeles), editado por Keith Bromley. SPIE, 1986. http://dx.doi.org/10.1117/12.960506.

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Tinnirello, Alicia María, Eduardo Alberto Gago y Paola Andrea Szekieta. "ALGORITHMIC MATHEMATICS IN LINEAR ALGEBRA APPLICATIONS". En 12th International Technology, Education and Development Conference. IATED, 2018. http://dx.doi.org/10.21125/inted.2018.1738.

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Informes sobre el tema "Algebras, Linear Algorithms"

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Martín, A., L. Cirrottola, A. Froehly, R. Rossi y C. Soriano. D2.2 First release of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.010.

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This document presents a description of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh refinement (AMR) algorithms and implementations. The first one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with unfitted finite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is based on the use of an initial octree mesh that, after make it conforming through the addition of templatebased tetrahedral refinements, is adapted anisotropically during the calculation. Regarding the first strategy the following items are included:

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