Matrix Computations And Semiseparable Matrices

Author : Raf Vandebril,Marc Van Barel,Nicola Mastronardi
Publisher : JHUP
Page : 0 pages
File Size : 46,5 Mb
Release : 2007-12-18
Category : Mathematics
ISBN : 0801887143

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Matrix Computations and Semiseparable Matrices by Raf Vandebril,Marc Van Barel,Nicola Mastronardi Pdf

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

Author : Raf Vandebril,Marc Van Barel,Nicola Mastronardi
Publisher : JHU Press
Page : 516 pages
File Size : 54,6 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780801896804

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Matrix Computations and Semiseparable Matrices by Raf Vandebril,Marc Van Barel,Nicola Mastronardi Pdf

The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.

Author : Raf Vandebril,Marc Van Barel,Nicola Mastronardi
Publisher : JHUP
Page : 0 pages
File Size : 40,8 Mb
Release : 2007-12-18
Category : Mathematics
ISBN : 0801887143

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Matrix Computations and Semiseparable Matrices by Raf Vandebril,Marc Van Barel,Nicola Mastronardi Pdf

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

Author : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 734 pages
File Size : 42,6 Mb
Release : 1996-10-15
Category : Mathematics
ISBN : 0801854148

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Matrix Computations by Gene H. Golub,Charles F. Van Loan Pdf

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Author : Thomas F. Coleman,Charles Van Loan
Publisher : SIAM
Page : 271 pages
File Size : 40,6 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 1611971047

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Handbook for Matrix Computations by Thomas F. Coleman,Charles Van Loan Pdf

Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.

Author : Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan
Publisher : Springer
Page : 406 pages
File Size : 52,5 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9783319498874

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Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications by Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan Pdf

Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.

Author : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 781 pages
File Size : 46,8 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9781421408590

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Matrix Computations by Gene H. Golub,Charles F. Van Loan Pdf

A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

Author : James R. Bunch,Donald J. Rose
Publisher : Academic Press
Page : 468 pages
File Size : 53,6 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 : John Rischard Rice
Publisher : McGraw-Hill Companies
Page : 280 pages
File Size : 50,6 Mb
Release : 1981
Category : Computers
ISBN : UOM:39015000961592

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Matrix Computations and Mathematical Software by John Rischard Rice Pdf

Linear algebra background; types and sources of matrix computational problems; type of matrix that arise; gauss elimination and LU factorization; mathematical software objectives; mathematical software performance evaluation; how do you know you have right answers?; conditioning and backward error analysis; iterative methods; linear least squares and regression; projects; standard linear algebra software.

Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 54,8 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 : Efstratios Gallopoulos,Bernard Philippe,Ahmed H. Sameh
Publisher : Springer
Page : 489 pages
File Size : 55,5 Mb
Release : 2015-07-25
Category : Technology & Engineering
ISBN : 9789401771887

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Parallelism in Matrix Computations by Efstratios Gallopoulos,Bernard Philippe,Ahmed H. Sameh Pdf

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.

Author : G. W. Stewart
Publisher : SIAM
Page : 476 pages
File Size : 49,7 Mb
Release : 1998-08-01
Category : Mathematics
ISBN : 9780898714142

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Matrix Algorithms by G. W. Stewart Pdf

This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.

Author : Gene Howard Golub,Charles F. Van Loan
Publisher : Unknown
Page : 702 pages
File Size : 52,9 Mb
Release : 2007
Category : Electronic
ISBN : 8185931720

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Matrix Computations (3/e) by Gene Howard Golub,Charles F. Van Loan Pdf

Author : Gilbert W. Stewart
Publisher : Academic Press
Page : 462 pages
File Size : 47,7 Mb
Release : 1973-05-28
Category : Computers
ISBN : UOM:39015014362415

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Introduction to Matrix Computations by Gilbert W. Stewart Pdf

Preliminaries; Practicalities; The direct solution of linear systems; Norms, limits, and condition numbers; The linear least squares problem; Eigenvalues and eigenvectors; The QR algorithm; Appendices; Index.

Author : Raf Vandebril,Marc Van Barel,Nicola Mastronardi
Publisher : JHU Press
Page : 594 pages
File Size : 54,6 Mb
Release : 2008-01-14
Category : Mathematics
ISBN : 9780801896798

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Matrix Computations and Semiseparable Matrices by Raf Vandebril,Marc Van Barel,Nicola Mastronardi Pdf

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.