Cover for Applied Iterative Methods

Applied Iterative Methods

Book1981

Authors:

LOUIS A. HAGEMAN and DAVID M. YOUNG

Applied Iterative Methods

Book1981

 

Cover for Applied Iterative Methods

Authors:

LOUIS A. HAGEMAN and DAVID M. YOUNG

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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 gene ... read full description

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  2. Book chapterAbstract only

    CHAPTER 1 - Background on Linear Algebra and Related Topics

    Pages 1-17

  3. Book chapterAbstract only

    CHAPTER 2 - Background on Basic Iterative Methods

    Pages 18-38

  4. Book chapterAbstract only

    CHAPTER 3 - Polynomial Acceleration

    Pages 39-44

  5. Book chapterAbstract only

    CHAPTER 4 - Chebyshev Acceleration

    Pages 45-58

  6. Book chapterAbstract only

    CHAPTER 5 - An Adaptive Chebyshev Procedure Using Special Norms

    Pages 59-92

  7. Book chapterAbstract only

    CHAPTER 6 - Adaptive Chebyshev Acceleration

    Pages 93-137

  8. Book chapterAbstract only

    CHAPTER 7 - Conjugate Gradient Acceleration

    Pages 138-161

  9. Book chapterAbstract only

    CHAPTER 8 - Special Methods for Red/Black Partitionings

    Pages 162-208

  10. Book chapterAbstract only

    CHAPTER 9 - Adaptive Procedures for the Successive Overrelaxation Method

    Pages 209-258

  11. Book chapterAbstract only

    CHAPTER 10 - The Use of Iterative Methods in the Solution of Partial Differential Equations

    Pages 259-286

  12. Book chapterAbstract only

    CHAPTER 11 - Case Studies

    Pages 287-329

  13. Book chapterAbstract only

    CHAPTER 12 - The Nonsymmetrizable Case

    Pages 330-356

  14. Book chapterNo access

    APPENDIX A - Chebyshev Acceleration Subroutine

    Pages 357-362

  15. Book chapterNo access

    APPENDIX B - CCSI Subroutine

    Pages 363-367

  16. Book chapterNo access

    APPENDIX C - SOR Subroutine

    Pages 368-372

  17. Book chapterNo access

    Bibliography

    Pages 373-380

  18. Book chapterNo access

    Index

    Pages 381-386

  19. Book chapterNo access

    Computer Science and Applied Mathematics: A SERIES OF MONOGRAPHS AND TEXTBOOKS

    Pages 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

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Authors

LOUIS A. HAGEMAN

Westinghouse Electric Corporation, West Mifflin, Pennsylvania

DAVID M. YOUNG

Center for Numerical Analysis, The University of Texas at Austin, Austin, Texas