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© 2016

Parallelism in Matrix Computations

Textbook

Part of the Scientific Computation book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages i-xxx
  2. Basics

    1. Front Matter
      Pages 1-1
    2. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 3-16
    3. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 17-45
  3. Dense and Special Matrix Computations

    1. Front Matter
      Pages 47-47
    2. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 49-78
    3. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 79-89
    4. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 91-163
    5. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 165-225
    6. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 227-247
    7. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 249-274
  4. Sparse Matrix Computations

    1. Front Matter
      Pages 275-275
    2. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 277-310
    3. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 311-341
    4. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 343-405
  5. Matrix Functions and Characteristics

    1. Front Matter
      Pages 407-407
    2. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 409-438
    3. Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
      Pages 439-465
  6. Back Matter
    Pages 467-473

About this book

Introduction

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.

Keywords

BLAS computing Davidson methods Dense matrix computations GramSchmidt orthogonalization Grid based methods LU factorization Lanczos method Matrix dimensionality reduction Sparse matrix computations Trace minimization method

Authors and affiliations

  1. 1.Computer Engineering and InformaticsUniversity of PatrasPatrasGreece
  2. 2.Campus de BeaulieuINRIA/IRISARennes CedexFrance
  3. 3.Dept. of Computer SciencePurdue UniversityWest LafayetteUSA

About the authors

Efstratios Gallopoulos, University of Patras, Patras Greece
Bernard Philippe, INRIA/IRISA, Rennes Cedex, France
Ahmed H. Sameh, Purdue University, West Lafayette, IN, USA

Bibliographic information

Reviews

“The exposition of the material is always very clear. The book is written confidently, with the greatest expertise and a remarkable breadth of topics. It should be an excellent resource for a broad audience of applied mathematicians. I would recommended it to all students, engineers and researchers in applied mathematics who wish to learn something about modern parallel techniques for large-scale matrix computation. Kudos to the authors on having produced such a delightful read and a much-needed reference!” (Bruno Carpentieri, Mathematical Reviews, 2017)

“The goal of this book is to provide basic principles for the design of such efficient parallel algorithms for dense and sparse matrices. … The book is intended to be adequate for researchers as well as for advanced graduates.” (Gudula Rünger, zbMATH 1341.65011, 2016)

“This book covers parallel algorithms for a wide range of matrix computation problems, ranging from solving systems of linear equations to computing pseudospectra of matrices. … This is a valuable reference book for researchers and practitioners in parallel computing. It includes up-to-date and comprehensive lists of references for various topics. … this book is well written and accurate. I highly recommend it to the parallel computing community … .” (Sanzheng Qiao, Computing Reviews, November, 2015)