Direct Methods For Sparse Matrices

Author : Timothy A. Davis
Publisher : SIAM
Page : 228 pages
File Size : 53,5 Mb
Release : 2006-09-01
Category : Computers
ISBN : 9780898716139

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Direct Methods for Sparse Linear Systems by Timothy A. Davis Pdf

The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.

Author : I. S. Duff,A. M. Erisman,J. K. Reid
Publisher : Oxford University Press
Page : 416 pages
File Size : 54,5 Mb
Release : 2017-02-10
Category : Mathematics
ISBN : 9780192507518

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Direct Methods for Sparse Matrices by I. S. Duff,A. M. Erisman,J. K. Reid Pdf

The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Author : O. Osterby,Z. Zlatev
Publisher : Lecture Notes in Computer Science
Page : 142 pages
File Size : 48,9 Mb
Release : 1983-08
Category : Mathematics
ISBN : UCAL:B5008694

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Direct Methods for Sparse Matrices by O. Osterby,Z. Zlatev Pdf

Author : Timothy A. Davis
Publisher : SIAM
Page : 229 pages
File Size : 55,7 Mb
Release : 2006-01-01
Category : Computers
ISBN : 0898718880

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Direct Methods for Sparse Linear Systems by Timothy A. Davis Pdf

Presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.

Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 51,7 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Mathematics of Computing -- General.

Author : Iain S. Duff
Publisher : Unknown
Page : 0 pages
File Size : 54,6 Mb
Release : 1989
Category : Electronic
ISBN : 0198543085

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Direct Methods for Sparse Matrices by Iain S. Duff Pdf

Author : Aarhus Universitet. Regionale EDB-center. Centre for Basic Research in Computer Science,O. Oesterby,Z. Zlatev
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 1980
Category : Sparse matrices
ISBN : OCLC:10766701

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Direct methods for sparse matrices by Aarhus Universitet. Regionale EDB-center. Centre for Basic Research in Computer Science,O. Oesterby,Z. Zlatev Pdf

Author : Sergio Pissanetzky
Publisher : Academic Press
Page : 336 pages
File Size : 42,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483270401

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Sparse Matrix Technology by Sergio Pissanetzky Pdf

Sparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology. The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and computational techniques needed for sparse matrix technology; sparse matrix methods and algorithms for the direct solution of linear equations; and algorithms for different purposes connected with sparse matrix technology. Engineers, programmers, analysts, teachers, and students in the computer sciences will find the book interesting.

Author : Zahari Zlatev
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 51,9 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9789401711166

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Computational Methods for General Sparse Matrices by Zahari Zlatev Pdf

'Et moi ... - si j'avait su comment en revenir, One service mathematics has rendered the je n 'y serais point aile.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.

Author : James R. Bunch,Donald J. Rose
Publisher : Academic Press
Page : 468 pages
File Size : 52,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483263403

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Sparse Matrix Computations by James R. Bunch,Donald J. Rose Pdf

Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

Author : Kurt Antreich
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 43,6 Mb
Release : 2003
Category : Mathematics
ISBN : 376432192X

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Modelling, Simulation and Optimization of Integrated Circuits by Kurt Antreich Pdf

In November 2001 the Mathematical Research Center at Oberwolfach, Germany, hosted the third Conference on Mathematical Models and Numerical Simulation in Electronic Industry. It brought together researchers in mathematics, electrical engineering and scientists working in industry.The contributions to this volume try to bridge the gap between basic and applied mathematics, research in electrical engineering and the needs of industry.

Author : Per-Gunnar Martinsson
Publisher : SIAM
Page : 332 pages
File Size : 51,8 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9781611976045

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Fast Direct Solvers for Elliptic PDEs by Per-Gunnar Martinsson Pdf

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Author : Lars Elden
Publisher : SIAM
Page : 226 pages
File Size : 50,6 Mb
Release : 2007-07-12
Category : Computers
ISBN : 9780898716269

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Matrix Methods in Data Mining and Pattern Recognition by Lars Elden Pdf

Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.

Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 52,5 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783319050898

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Numerical Methods in Matrix Computations by Åke Björck Pdf

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Author : Yousef Saad
Publisher : SIAM
Page : 292 pages
File Size : 46,5 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 1611970733

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Numerical Methods for Large Eigenvalue Problems by Yousef Saad Pdf

This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.