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### Table of contents

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#### CHAPTER 1 - Background on Linear Algebra and Related Topics

Pages 1-17 - Book chapterAbstract only
#### CHAPTER 2 - Background on Basic Iterative Methods

Pages 18-38 - Book chapterAbstract only
#### CHAPTER 3 - Polynomial Acceleration

Pages 39-44 - Book chapterAbstract only
#### CHAPTER 4 - Chebyshev Acceleration

Pages 45-58 - Book chapterAbstract only
#### CHAPTER 5 - An Adaptive Chebyshev Procedure Using Special Norms

Pages 59-92 - Book chapterAbstract only
#### CHAPTER 6 - Adaptive Chebyshev Acceleration

Pages 93-137 - Book chapterAbstract only
#### CHAPTER 7 - Conjugate Gradient Acceleration

Pages 138-161 - Book chapterAbstract only
#### CHAPTER 8 - Special Methods for Red/Black Partitionings

Pages 162-208 - Book chapterAbstract only
#### CHAPTER 9 - Adaptive Procedures for the Successive Overrelaxation Method

Pages 209-258 - Book chapterAbstract only
#### CHAPTER 10 - The Use of Iterative Methods in the Solution of Partial Differential Equations

Pages 259-286 - Book chapterAbstract only
#### CHAPTER 11 - Case Studies

Pages 287-329 - Book chapterAbstract only
#### CHAPTER 12 - The Nonsymmetrizable Case

Pages 330-356 - Book chapterNo access
#### APPENDIX A - Chebyshev Acceleration Subroutine

Pages 357-362 - Book chapterNo access
#### APPENDIX B - CCSI Subroutine

Pages 363-367 - Book chapterNo access
#### APPENDIX C - SOR Subroutine

Pages 368-372 - Book chapterNo access
#### Bibliography

Pages 373-380 - Book chapterNo access
#### Index

Pages 381-386 - Book chapterNo access
**Computer Science and Applied Mathematics**: A SERIES OF MONOGRAPHS AND TEXTBOOKSPages ibc1-ibc2

## About the book

### Description

Applied Iterative Methods discusses the practical utilization of iterative methods for solving large, sparse systems of linear algebraic equations. The book explains different general methods to present computational procedures to automatically determine favorable estimates of any iteration parameters, as well as when to stop the iterative process. The text also describes the utilization of iterative methods to solve multidimensional boundary-value problems (such as discretization stencil, mesh structure, or matrix partitioning) which affect the cost-effectiveness of iterative solution procedures. The book cites case studies involving iterative methods applications, including those concerning only three particular boundary-value problems. The text explains polynomial acceleration procedures (for example, Chebyshev acceleration and conjugate gradient acceleration) which can be applied to certain basic iterative methods or to the successive overtaxation (SOR) method. The book presents other case studies using the iterative methods to solve monoenergetic transport and nonlinear network flow multidimensional boundary-value problems. The text also describes the procedures for accelerating basic iterative methods which are not symmetrizable. The book will prove beneficial for mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

Applied Iterative Methods discusses the practical utilization of iterative methods for solving large, sparse systems of linear algebraic equations. The book explains different general methods to present computational procedures to automatically determine favorable estimates of any iteration parameters, as well as when to stop the iterative process. The text also describes the utilization of iterative methods to solve multidimensional boundary-value problems (such as discretization stencil, mesh structure, or matrix partitioning) which affect the cost-effectiveness of iterative solution procedures. The book cites case studies involving iterative methods applications, including those concerning only three particular boundary-value problems. The text explains polynomial acceleration procedures (for example, Chebyshev acceleration and conjugate gradient acceleration) which can be applied to certain basic iterative methods or to the successive overtaxation (SOR) method. The book presents other case studies using the iterative methods to solve monoenergetic transport and nonlinear network flow multidimensional boundary-value problems. The text also describes the procedures for accelerating basic iterative methods which are not symmetrizable. The book will prove beneficial for mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

## Details

### ISBN

978-0-12-313340-3

### Language

English

### Published

1981

### Copyright

Copyright © 1981 Elsevier Inc. All rights reserved.

### Imprint

Academic Press