Iterative Solution of Large Sparse Systems of Equations / Edition 1

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Overview

This book presents the description of the state of modern iterative techniques together with systematic analysis. The first chapters discuss the classical methods. Comprehensive chapters are devoted to semi-iterative techniques (Chebyshev methods), transformations, incomplete decompositions, gradient and conjugate gradient methods, multi-grid methods and domain decomposition techniques (including e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.
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Editorial Reviews

Booknews
Translated from the German edition. The author describes the recent state of iterative and related methods without delving into specialized areas. Pascal programs are explicitly given and a collection of the source codes are available on disk from the author. Topics include analysis in the 2-cycle case, analysis for m- matrices, semi-iterative methods, transformations, secondary iterations, incomplete triangular decompositions, conjugate gradient methods, multi-grid methods, and domain decomposition methods. Exercises are included. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780387940649
  • Publisher: Springer New York
  • Publication date: 11/29/1993
  • Series: Applied Mathematical Sciences Series , #95
  • Edition description: 1994
  • Edition number: 1
  • Pages: 460
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.06 (d)

Table of Contents

Preface
Hints for Reading the Book
Notations
1 Introduction 1
2 Recapitulation of Linear Algebra 12
3 Iterative Methods 43
4 Methods of Jacobi and Gauss-Seidel and SOR Iteration in the Positive Definite Case 65
5 Analysis in the 2-Cyclic Case 122
6 Analysis for M-Matrices 144
7 Semi-Iterative Methods 165
8 Transformations, Secondary Iterations, Incomplete Triangular Decompositions 205
9 Conjugate Gradient Methods 248
10 Multi-Grid Methods 296
11 Domain Decomposition Methods 367
Bibliography 405
Subject Index 418
Index of PASCAL Terms 426
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