Matrix Computations

  • Filename: matrix-computations.
  • ISBN: 0801854148
  • Release Date: 1996-10-15
  • Number of pages: 694
  • Author: Gene H. Golub
  • Publisher: JHU Press

"An invaluable reference book that should be in every university library." -- Image: Bulletin of the International Linear Algebra Society

Sparse Matrices

  • Filename: sparse-matrices.
  • ISBN: 9780080956084
  • Release Date: 1973-05-11
  • Number of pages: 159
  • Author: Tewarson
  • Publisher: Academic Press

Sparse Matrices

Parallelism in Matrix Computations

  • Filename: parallelism-in-matrix-computations.
  • ISBN: 9789401771887
  • Release Date: 2015-07-25
  • Number of pages: 473
  • Author: Efstratios Gallopoulos
  • Publisher: Springer

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.

Fundamentals of Matrix Computations

  • Filename: fundamentals-of-matrix-computations.
  • ISBN: 9780471461678
  • Release Date: 2004-08-27
  • Number of pages: 640
  • Author: David S. Watkins
  • Publisher: John Wiley & Sons

A significantly revised and improved introduction to a critical aspect of scientific computation Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights. This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes: * Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations * Early introduction of the singular value decomposition * A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems * An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.

Sparse and Parallel Matrix Computations

  • Filename: sparse-and-parallel-matrix-computations.
  • ISBN: STANFORD:36105025674099
  • Release Date: 1978
  • Number of pages: 318
  • Author: Stanford University. Computer Science Dept
  • Publisher:

This thesis deals with four important matrix problems: the application of many variants of the conjugate gradient method for solving matrix equations, the solution of lower and upper bounds guadratic programs associated with M-matrices, the construction of a Block Lanczos method for computing the greatest singular values of a matrix, and the computation of the singular value decomposition of a matrix on the ILLIAC-IV computer. (Author).

Matrix Computations

  • Filename: matrix-computations.
  • ISBN: 9781421407944
  • Release Date: 2012-12-27
  • Number of pages: 756
  • Author: Gene H. Golub
  • Publisher: JHU Press

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.

Numerical Methods in Matrix Computations

  • Filename: numerical-methods-in-matrix-computations.
  • ISBN: 9783319050898
  • Release Date: 2014-10-07
  • Number of pages: 800
  • Author: Åke Björck
  • Publisher: Springer

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. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

Computational Methods for Large Sparse Power Systems Analysis

  • Filename: computational-methods-for-large-sparse-power-systems-analysis.
  • ISBN: 0792375912
  • Release Date: 2002
  • Number of pages: 333
  • Author: S. A. Soman
  • Publisher: Springer Science & Business Media

Computational methods in Power Systems require significant inputs from diverse disciplines, such as data base structures, numerical analysis etc. Strategic decisions in sparsity exploitation and algorithm design influence large-scale simulation and high-speed computations. Selection of programming paradigm shapes the design, its modularity and reusability. This has a far reaching effect on software maintenance. Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach provides a unified object oriented (OO) treatment for power system analysis. Sparsity exploitation techniques in OO paradigm are emphasized to facilitate large scale and fast computing. Specific applications like large-scale load flow, short circuit analysis, state estimation and optimal power flow are discussed within this framework. A chapter on modeling and computational issues in power system dynamics is also included. Motivational examples and illustrations are included throughout the book. A library of C++ classes provided along with this book has classes for transmission lines, transformers, substation etc. A CD-ROM with C++ programs is also included. It contains load flow, short circuit analysis and network topology processor applications. Power system data is provided and systems up to 150 buses can be studied. Other Special Features: This book is the first of its kind, covering power system applications designed with an OO perspective. Chapters on object orientation for modeling of power system computations, data structure, large sparse linear system solver, sparse QR decomposition in an OO framework are special features of this book.

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