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Computer Algorithms for Solving Linear Algebraic Equations

The State of the Art

  • Conference proceedings
  • © 1991

Overview

Editors:
  1. Emilio Spedicato

    1. Department of Mathematics, University of Bergamo, Bergamo, Italy

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Part of the book series: NATO ASI Subseries F: (NATO ASI F, volume 77)

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Table of contents (14 papers)

  1. Front Matter

    Pages I-VIII
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  2. Classical Methods for Linear Equations

    • C. G. Broyden
    Pages 1-26

  3. Complexity of Algorithms for Linear Systems of Equations

    • Victor Pan
    Pages 27-56

  4. Algorithms for Linear Least Squares Problems

    • Ã…. Björck
    Pages 57-92

  5. Abs Algorithms for General Linear Systems

    • E. Spedicato
    Pages 93-110

  6. ABS Algorithms for Sparse Linear Systems

    • Jozsef Abaffy
    Pages 111-131

  7. Multi-Grid Algorithms

    • W. Hackbusch
    Pages 133-160

  8. Two Multi-Level Methods for Nonuniformly Refined Grids

    • Harry Yserentant
    Pages 161-167

  9. Preconditioning methods for block H-matrices

    • Owe Axelsson
    Pages 169-184

  10. Domain Decomposition methods for solving large sparse linear systems

    • Gérard Meurant
    Pages 185-206

  11. A Splitting Method for Large Sparse Linear Systems on a Multivector Computer

    • Ilio Galligani
    Pages 207-215

  12. Scheduling Parallel Factorization Algorithms on a Shared Memory Computer

    • Michel Cosnard
    Pages 217-252

  13. Gaussian elimination on distributed memory architectures

    • Yves Robert
    Pages 253-276

  14. Parallel Algorithms for General Sparse Systems

    • Iain S. Duff
    Pages 277-297

  15. The Solution of Partially Separable Linear Equations on Parallel Processing Systems

    • L. C. W. Dixon
    Pages 299-338

  16. Back Matter

    Pages 339-356
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Keywords

About this book

The NATO Advanced Study Institute on "Computer algorithms for solving linear algebraic equations: the state of the art" was held September 9-21, 1990, at II Ciocco, Barga, Italy. It was attended by 68 students (among them many well known specialists in related fields!) from the following countries: Belgium, Brazil, Canada, Czechoslovakia, Denmark, France, Germany, Greece, Holland, Hungary, Italy, Portugal, Spain, Turkey, UK, USA, USSR, Yugoslavia. Solving linear equations is a fundamental task in most of computational mathematics. Linear systems which are now encountered in practice may be of very large dimension and their solution can still be a challenge in terms of the requirements of accuracy or reasonable computational time. With the advent of supercomputers with vector and parallel features, algorithms which were previously formulated in a framework of sequential operations often need a completely new formulation, and algorithms that were not recommended in a sequential framework may become the best choice. The aim of the ASI was to present the state of the art in this field. While not all important aspects could be covered (for instance there is no presentation of methods using interval arithmetic or symbolic computation), we believe that most important topics were considered, many of them by leading specialists who have contributed substantially to the developments in these fields.

Editors and Affiliations

  • Department of Mathematics, University of Bergamo, Bergamo, Italy

    Emilio Spedicato

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