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Dissertations / Theses on the topic 'Randomized Numerical Linear Algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Musco, Cameron N. (Cameron Nicholas). "The power of randomized algorithms : from numerical linear algebra to biological systems." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120424.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 323-347).<br>In this thesis we study simple, randomized algorithms from a dual perspective. The first part of the work considers how randomized methods can be used to accelerate the solution of core problems in numerical linear algebra. In particular, we give a randomized low-rank approximation algorithm for positive semidefinite matrices that runs in sublinear time, significantly improving

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2

Wilkerson, Owen Tanner. "Fast, Sparse Matrix Factorization and Matrix Algebra via Random Sampling for Integral Equation Formulations in Electromagnetics." UKnowledge, 2019. https://uknowledge.uky.edu/ece_etds/147.

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Many systems designed by electrical & computer engineers rely on electromagnetic (EM) signals to transmit, receive, and extract either information or energy. In many cases, these systems are large and complex. Their accurate, cost-effective design requires high-fidelity computer modeling of the underlying EM field/material interaction problem in order to find a design with acceptable system performance. This modeling is accomplished by projecting the governing Maxwell equations onto finite dimensional subspaces, which results in a large matrix equation representation (Zx = b) of the EM problem

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DiPaolo, Conner. "Randomized Algorithms for Preconditioner Selection with Applications to Kernel Regression." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/230.

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The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M-1A ||F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which suggests the quantity is im

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Balabanov, Oleg. "Randomized linear algebra for model order reduction." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/668906.

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Solutions to high-dimensional parameter-dependent problems are in great demand in the contemporary applied science and engineering. The standard approximation methods for parametric equations can require computational resources that are exponential in the dimension of the parameter space, which is typically refereed to as the curse of dimensionality. To break the curse of dimensionality one has to appeal to nonlinear methods that exploit the structure of the solution map, such as projection-based model order reduction methods. This thesis proposes novel methods based on randomized linear a

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5

Battles, Zachary. "Numerical linear algebra for continuous functions." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427900.

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6

Higham, N. J. "Nearness problems in numerical linear algebra." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374580.

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7

Zounon, Mawussi. "On numerical resilience in linear algebra." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0038/document.

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Comme la puissance de calcul des systèmes de calcul haute performance continue de croître, en utilisant un grand nombre de cœurs CPU ou d’unités de calcul spécialisées, les applications hautes performances destinées à la résolution des problèmes de très grande échelle sont de plus en plus sujettes à des pannes. En conséquence, la communauté de calcul haute performance a proposé de nombreuses contributions pour concevoir des applications tolérantes aux pannes. Cette étude porte sur une nouvelle classe d’algorithmes numériques de tolérance aux pannes au niveau de l’application qui ne nécessite p

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Kannan, Ramaseshan. "Numerical linear algebra problems in structural analysis." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/numerical-linear-algebra-problems-in-structural-analysis(7df0f708-fc12-4807-a1f5-215960d9c4d4).html.

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A range of numerical linear algebra problems that arise in finite element-based structural analysis are considered. These problems were encountered when implementing the finite element method in the software package Oasys GSA. We present novel solutions to these problems in the form of a new method for error detection, algorithms with superior numerical effeciency and algorithms with scalable performance on parallel computers. The solutions and their corresponding software implementations have been integrated into GSA's program code and we present results that demonstrate the use of these impl

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9

Gulliksson, Rebecka. "A comparison of parallelization approaches for numerical linear algebra." Thesis, Umeå universitet, Institutionen för datavetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-81116.

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The efficiency of numerical libraries for a given computation is highly dependent on the size of the inputs. For very small inputs it is expected that LAPACK combined with BLAS is the superior alternative, while the new generation of parallelized numerical libraries (such as PLASMA and SuperMatrix) is expected to be superior for large inputs. In between these two extremes in input sizes, there might exist a niche for a new class of numerical libraries.In this thesis a prototype library, targeting medium sized inputs, is presented. The prototype library uses a mixed data and task parallel appro

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10

Song, Zixu. "Software engineering abstractions for a numerical linear algebra library." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/software-engineering-abstractions-for-a-numerical-linear-algebra-library(68304a9b-56db-404b-8ffb-4613f5102c1a).html.

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This thesis aims at building a numerical linear algebra library with appropriate software engineering abstractions. Three areas of knowledge, namely, Numerical Linear Algebra (NLA), Software Engineering and Compiler Optimisation Techniques, are involved. Numerical simulation is widely used in a large number of distinct disciplines to help scientists understand and discover the world. The solutions to frequently occurring numerical problems have been implemented in subroutines, which were then grouped together to form libraries for ease of use. The design, implementation and maintenance of a NL

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11

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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Zhu, Shengxin. "Numerical linear approximation involving radial basis functions." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:b870646b-5155-45f8-b38c-ae6cf4d22f27.

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This thesis aims to acquire, deepen and promote understanding of computing techniques for high dimensional scattered data approximation with radial basis functions. The main contributions of this thesis include sufficient conditions for the sovability of compactly supported radial basis functions with different shapes, near points preconditioning techniques for high dimensional interpolation systems with compactly supported radial basis functions, a heterogeneous hierarchical radial basis function interpolation scheme, which allows compactly supported radial basis functions of different shapes

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13

Kaya, Dogan. "Parallel algorithms for numerical linear algebra on a shared memory multiprocessor." Thesis, University of Newcastle Upon Tyne, 1995. http://hdl.handle.net/10443/2008.

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This thesis discusses a variety of parallel algorithms for linear algebra problems including the solution of the linear system of equations Ax = b using QR and L U decomposition, reduction of a general matrix A to Hessenberg form, reduction of a real symmetric matrix B to tridiagonal form, and solution of the symmetric tridiagonal eigenproblem. Empirical comparisons are carried out using various different versions of the above algorithms and this is described in this thesis. We also compare three different synchronisation mechanisms when applied to the reduction to Hessenberg form problem. We

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Nguyen, Hong Diep. "Efficient algorithms for verified scientific computing : Numerical linear algebra using interval arithmetic." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00680352.

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Interval arithmetic is a means to compute verified results. However, a naive use of interval arithmetic does not provide accurate enclosures of the exact results. Moreover, interval arithmetic computations can be time-consuming. We propose several accurate algorithms and efficient implementations in verified linear algebra using interval arithmetic. Two fundamental problems are addressed, namely the multiplication of interval matrices and the verification of a floating-point solution of a linear system. For the first problem, we propose two algorithms which offer new tradeoffs between speed an

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Phillips, Adam. "GPU Accelerated Approach to Numerical Linear Algebra and Matrix Analysis with CFD Applications." Honors in the Major Thesis, University of Central Florida, 2014. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1635.

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A GPU accelerated approach to numerical linear algebra and matrix analysis with CFD applications is presented. The works objectives are to (1) develop stable and efficient algorithms utilizing multiple NVIDIA GPUs with CUDA to accelerate common matrix computations, (2) optimize these algorithms through CPU/GPU memory allocation, GPU kernel development, CPU/GPU communication, data transfer and bandwidth control to (3) develop parallel CFD applications for Navier Stokes and Lattice Boltzmann analysis methods. Special consideration will be given to performing the linear algebra algorithms under c

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Theveny, Philippe. "Numerical Quality and High Performance In Interval Linear Algebra on Multi-Core Processors." Thesis, Lyon, École normale supérieure, 2014. http://www.theses.fr/2014ENSL0941/document.

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L'objet est de comparer des algorithmes de multiplication de matrices à coefficients intervalles et leurs implémentations.Le premier axe est la mesure de la précision numérique. Les précédentes analyses d'erreur se limitent à établir une borne sur la surestimation du rayon du résultat en négligeant les erreurs dues au calcul en virgule flottante. Après examen des différentes possibilités pour quantifier l'erreur d'approximation entre deux intervalles, l'erreur d'arrondi est intégrée dans l'erreur globale. À partir de jeux de données aléatoires, la dispersion expérimentale de l'erreur globale p

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Shikongo, Albert. "Numerical Treatment of Non-Linear singular pertubation problems." Thesis, Online access, 2007. http://etd.uwc.ac.za/usrfiles/modules/etd/docs/etd_gen8Srv25Nme4_3831_1257936459.pdf.

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18

Wu, Wei. "Paving the Randomized Gauss-Seidel." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/scripps_theses/1074.

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The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the

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Waldherr, Konrad [Verfasser]. "Numerical Linear and Multilinear Algebra in Quantum Control and Quantum Tensor Networks / Konrad Waldherr." München : Verlag Dr. Hut, 2014. http://d-nb.info/1064560601/34.

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Wan, Dejun. "The Randomized Kaczmarz Method with Application on Making Macroeconomic Predictions." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/cmc_theses/1437.

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This paper will demonstrate the principles and important facts of the randomized Kaczmarz algorithm as well as its extended version proposed by Zouzias and Ferris. Through the analysis made by Strohmer and Vershynin as well as Needell, it can be shown that the randomized Kaczmarz method is theoretically applicable in solving over-determined linear systems with or without noise. The extension of the randomized Kaczmarz algorithm further applies to the linear systems with non-unique solutions. In the experiment section of this paper, we compare the accuracies of the algorithms discussed in the p

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21

Najahi, Mohamed amine. "Synthesis of certified programs in fixed-point arithmetic, and its application to linear algebra basic blocks : and its application to linear algebra basic blocks." Thesis, Perpignan, 2014. http://www.theses.fr/2014PERP1212.

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Pour réduire les coûts des systèmes embarqués, ces derniers sont livrés avec des micro-processeurs peu puissants. Ces processeurs sont dédiés à l'exécution de tâches calculatoires dont certaines, comme la transformée de Fourier rapide, peuvent s'avérer exigeantes en termes de ressources de calcul. Afin que les implémentations de ces algorithmes soient efficaces, les programmeurs utilisent l'arithmétique à virgule fixe qui est plus adaptée aux processeurs dépourvus d'unité flottante. Cependant, ils se retrouvent confrontés à deux difficultés: D'abord, coder en virgule fixe est fastidieux et exi

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Takahashi, Ryan. "Structured Matrices and the Algebra of Displacement Operators." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/45.

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Matrix calculations underlie countless problems in science, mathematics, and engineering. When the involved matrices are highly structured, displacement operators can be used to accelerate fundamental operations such as matrix-vector multiplication. In this thesis, we provide an introduction to the theory of displacement operators and study the interplay between displacement and natural matrix constructions involving direct sums, Kronecker products, and blocking. We also investigate the algebraic behavior of displacement operators, developing results about invertibility and kernels.

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23

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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Mathematics<br>Ph.D.<br>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 gene

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24

Kaperick, Bryan James. "Diagonal Estimation with Probing Methods." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/90402.

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Probing methods for trace estimation of large, sparse matrices has been studied for several decades. In recent years, there has been some work to extend these techniques to instead estimate the diagonal entries of these systems directly. We extend some analysis of trace estimators to their corresponding diagonal estimators, propose a new class of deterministic diagonal estimators which are well-suited to parallel architectures along with heuristic arguments for the design choices in their construction, and conclude with numerical results on diagonal estimation and ordering problems, demonstr

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25

Rubensson, Emanuel H. "Matrix Algebra for Quantum Chemistry." Doctoral thesis, Stockholm : Bioteknologi, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9447.

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Fasi, Massimiliano. "Weighted geometric mean of large-scale matrices: numerical analysis and algorithms." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8274/.

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Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition

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27

Sète, Olivier [Verfasser], Jörg [Akademischer Betreuer] Liesen, Jörg [Gutachter] Liesen, Reinhard [Gutachter] Nabben, and Elias [Gutachter] Wegert. "On interpolation and approximation problems in numerical linear algebra / Olivier Sète ; Gutachter: Jörg Liesen, Reinhard Nabben, Elias Wegert ; Betreuer: Jörg Liesen." Berlin : Technische Universität Berlin, 2016. http://d-nb.info/1156018498/34.

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Eisenlohr, John Merrick. "Parallel ILU Preconditioning for Structured Grid Matrices." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429820221.

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Ladenheim, Scott Aaron. "Constraint Preconditioning of Saddle Point Problems." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/319906.

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Mathematics<br>Ph.D.<br>This thesis is concerned with the fast iterative solution of linear systems of equations of saddle point form. Saddle point problems are a ubiquitous class of matrices that arise in a host of computational science and engineering applications. The focus here is on improving the convergence of iterative methods for these problems by preconditioning. Preconditioning is a way to transform a given linear system into a different problem for which iterative methods converge faster. Saddle point matrices have a very specific block structure and many preconditioning strategies

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Zhang, Weijian. "Evolving graphs and similarity-based graphs with applications." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/evolving-graphs-and-similaritybased-graphs-with-applications(66a23d3d-1ad0-454b-9ba0-175b566af95d).html.

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A graph is a mathematical structure for modelling the pairwise relations between objects. This thesis studies two types of graphs, namely, similarity-based graphs and evolving graphs. We look at ways to traverse an evolving graph. In particular, we examine the influence of temporal information on node centrality. In the process, we develop EvolvingGraphs.jl, a software package for analyzing time-dependent networks. We develop Etymo, a search system for discovering interesting research papers. Etymo utilizes both similarity-based graphs and evolving graphs to build a knowledge graph of research

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Frazier, William. "Application of Symplectic Integration on a Dynamical System." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3213.

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Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating sol

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32

Sharify, Meisam. "Algorithmes de mise à l'échelle et méthodes tropicales en analyse numérique matricielle." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00643836.

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L'Algèbre tropicale peut être considérée comme un domaine relativement nouveau en mathématiques. Elle apparait dans plusieurs domaines telles que l'optimisation, la synchronisation de la production et du transport, les systèmes à événements discrets, le contrôle optimal, la recherche opérationnelle, etc. La première partie de ce manuscrit est consacrée a l'étude des applications de l'algèbre tropicale à l'analyse numérique matricielle. Nous considérons tout d'abord le problème classique de l'estimation des racines d'un polynôme univarié. Nous prouvons plusieurs nouvelles bornes pour la valeur

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Pearson, John W. "Fast iterative solvers for PDE-constrained optimization problems." Thesis, University of Oxford, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.

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In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The sol

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Ishigami, Hiroyuki. "Studies on Parallel Solvers Based on Bisection and Inverse Iterationfor Subsets of Eigenpairs and Singular Triplets." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215685.

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5章（本文31～40ページ）と元となった論文の著作権はIEEEに属するため、規約に従い、本文79ページにおいて出典を示すともに、コピーライト表記を付している。本文39、40ページの全ての図の著作権は、IEEEに属する。このため、これら全ての図においてコピーライト表記を付している。<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(情報学)<br>甲第19858号<br>情博第609号<br>新制||情||106(附属図書館)<br>32894<br>京都大学大学院情報学研究科数理工学専攻<br>(主査)教授中村佳正, 教授梅野健, 教授中島浩<br>学位規則第4条第1項該当

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Lacoursière, Claude. "Ghosts and machines : regularized variational methods for interactive simulations of multibodies with dry frictional contacts." Doctoral thesis, Umeå University, Computing Science, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1143.

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<p>A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers e

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Shen, Chong. "Topic Analysis of Tweets on the European Refugee Crisis Using Non-negative Matrix Factorization." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/cmc_theses/1388.

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The ongoing European Refugee Crisis has been one of the most popular trending topics on Twitter for the past 8 months. This paper applies topic modeling on bulks of tweets to discover the hidden patterns within these social media discussions. In particular, we perform topic analysis through solving Non-negative Matrix Factorization (NMF) as an Inexact Alternating Least Squares problem. We accelerate the computation using techniques including tweet sampling and augmented NMF, compare NMF results with different ranks and visualize the outputs through topic representation and frequency plots. We

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Tisseur, Françoise. "Méthodes numériques pour le calcul d'éléments spectraux : étude de la précision, la stabilité et la parallélisation." Saint-Etienne, 1997. http://www.theses.fr/1997STET4006.

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Cette thèse est constituée de deux parties. La première traite de la méthode QR pour le calcul de valeurs propres de matrices quelconques, de tailles modérées. Les contributions originales à ce sujet sont a) une preuve rigoureuse de sa stabilité inverse, b) un nouveau critère d'arrêt justifié par une analyse mathématique. La seconde partie traite de la méthode de Yau et Lu pour le calcul de valeurs propres de matrices symétriques réelles de grandes tailles. Les contributions dans ce travail à ce sujet sont a) une compréhension mathématique accrue de la méthode, b) sa validation numérique, c) u

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Srđan, Milićević. "Algorithms for computing the optimal Geršgorin-type localizations." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2020. https://www.cris.uns.ac.rs/record.jsf?recordId=114425&source=NDLTD&language=en.

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There are numerous ways to localize eigenvalues. One of the best known results is that the spectrum of a given matrix ACn,n is a subset of a union of discs centered at diagonal elements whose radii equal to the sum of the absolute values of the off-diagonal elements of a corresponding row in the matrix. This result (Ger&scaron;gorin's theorem, 1931) is one of the most important and elegant ways of eigenvalues localization ([63]). Among all Ger&scaron;gorintype sets, the minimal Ger&scaron;gorin set gives the sharpest and the most precise localization of the spectrum ([39]). In this thesis,

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Gittens, Alex A. "Topics in Randomized Numerical Linear Algebra." Thesis, 2013. https://thesis.library.caltech.edu/7880/13/ch1.pdf.

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<p>This thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices. </p> <p>Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contribute

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(9179300), Evgenia-Maria Kontopoulou. "RANDOMIZED NUMERICAL LINEAR ALGEBRA APPROACHES FOR APPROXIMATING MATRIX FUNCTIONS." Thesis, 2020.

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<p>This work explores how randomization can be exploited to deliver sophisticated</p><p>algorithms with provable bounds for: (i) The approximation of matrix functions, such</p><p>as the log-determinant and the Von-Neumann entropy; and (ii) The low-rank approximation</p><p>of matrices. Our algorithms are inspired by recent advances in Randomized</p><p>Numerical Linear Algebra (RandNLA), an interdisciplinary research area that exploits</p><p>randomization as a computational resource to develop improved algorithms for</p><p>large-scale linear algebra problems. The main goal of this work is to enc

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Zouzias, Anastasios. "Randomized Primitives For Linear Algebra and Applications." Thesis, 2013. http://hdl.handle.net/1807/36082.

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The present thesis focuses on the design and analysis of randomized algorithms for accelerating several linear algebraic tasks. In particular, we develop simple, efficient, randomized algorithms for a plethora of fundamental linear algebraic tasks and we also demonstrate their usefulness and applicability to matrix computations and graph theoretic problems. The thesis can be divided into three parts. The first part concentrates on the development of randomized linear algebraic primitives, the second part demonstrates the application of such primitives to matrix computations, and the last part

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Yamamoto, Yusaku. "High performance algorithms for numerical linear algebra." Thesis, 2003. http://hdl.handle.net/2237/6641.

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"High performance algorithms for numerical linear algebra." Thesis, 2003. http://hdl.handle.net/2237/6641.

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Luszczek, Piotr Rafal. "Performance improvements of common sparse numerical linear algebra computations." 2003. http://etd.utk.edu/2003/LuszczekPiotr.pdf.

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Thesis (Ph. D.)--University of Tennessee, Knoxville, 2003.<br>Title from title page screen (viewed Nov. 12, 2003). Thesis advisor: Dr. Jack J. Dongarra. Document formatted into pages (viii, 84 p. : ill.). Vita. Includes bibliographical references (p. 65-79).

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Kleinsteuber, Martin. "Jacobi-type methods on semisimple Lie algebras : a Lie algebraic approach to numerical linear algebra." Doctoral thesis, 2005. https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-16454.

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Es wird eine Lie-algebraische Verallgemeinerung sowohl des klassischen als auch des Sortier-Jacobi-Verfahrens für das symmetrische Eigenwertproblem behandelt. Der koordinatenfreie Zugang ermöglicht durch eine neue Betrachtungsweise die Vereinheitlichung strukturierter Eigen- und Singulärwertprobleme, darunter bis dato noch nicht betrachtete Fälle. Für beide Verfahren wird lokal quadratische Konvergenz, sowohl für den regulären als auch für den irregulären Fall, gezeigt. Die Analyse und Verallgemeinerung der sog. speziellen Sweeps für das symmetrische Eigenwertproblem führt zu neuen Sweep-Metho

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Abdelfattah, Ahmad. "Accelerating Scientific Applications using High Performance Dense and Sparse Linear Algebra Kernels on GPUs." Diss., 2015. http://hdl.handle.net/10754/346955.

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High performance computing (HPC) platforms are evolving to more heterogeneous configurations to support the workloads of various applications. The current hardware landscape is composed of traditional multicore CPUs equipped with hardware accelerators that can handle high levels of parallelism. Graphical Processing Units (GPUs) are popular high performance hardware accelerators in modern supercomputers. GPU programming has a different model than that for CPUs, which means that many numerical kernels have to be redesigned and optimized specifically for this architecture. GPUs usually outperform

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Boukaram, Wagih Halim. "Hierarchical Matrix Operations on GPUs." Diss., 2020. http://hdl.handle.net/10754/662664.

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Large dense matrices are ubiquitous in scientific computing, arising from the discretization of integral operators associated with elliptic pdes, Schur complement methods, covariances in spatial statistics, kernel-based machine learning, and numerical optimization problems. Hierarchical matrices are an efficient way for storing the dense matrices of very large dimension that appear in these and related settings. They exploit the fact that the underlying matrices, while formally dense, are data sparse. They have a structure consisting of blocks many of which can be well-approximated by lo

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Kleinsteuber, Martin [Verfasser]. "Jacobi-type methods on semisimple Lie algebras : a Lie algebraic approach to numerical linear algebra / vorgelegt von Martin Kleinsteuber." 2006. http://d-nb.info/979448603/34.

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Scoleri, Tony. "Fundamental numerical schemes for parameter estimation in computer vision." 2008. http://hdl.handle.net/2440/50726.

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An important research area in computer vision is parameter estimation. Given a mathematical model and a sample of image measurement data, key parameters are sought to encapsulate geometric properties of a relevant entity. An optimisation problem is often formulated in order to find these parameters. This thesis presents an elaboration of fundamental numerical algorithms for estimating parameters of multi-objective models of importance in computer vision applications. The work examines ways to solve unconstrained and constrained minimisation problems from the view points of theory, computationa

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Biswas, Prasenjit. "Hardware Consolidation Of Systolic Algorithms On A Coarse Grained Runtime Reconfigurable Architecture." Thesis, 2011. http://etd.iisc.ernet.in/handle/2005/2108.

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Application domains such as Bio-informatics, DSP, Structural Biology, Fluid Dynamics, high resolution direction finding, state estimation, adaptive noise cancellation etc. demand high performance computing solutions for their simulation environments. The core computations of these applications are in Numerical Linear Algebra (NLA) kernels. Direct solvers are predominantly required in the domains like DSP, estimation algorithms like Kalman Filter etc, where the matrices on which operations need to be performed are either small or medium sized, but dense. Faddeev's Algorithm is often used for so

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