Iterative Solution of Large Sparse Systems of Equations / Edition 1

by Wolfgang Hackbusch

Overview

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.

The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.

The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

Product Details

ISBN-13:	9781461287247
Publisher:	Springer New York
Publication date:	09/27/2011
Series:	Applied Mathematical Sciences , #95
Edition description:	Softcover reprint of the original 1st ed. 1994
Pages:	432
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About the Author

Wolfgang Hackbusch is a Professor in the Scientific Computing department at Max Planck Institute for Mathematics in the Sciences. His research areas include numerical treatment of partial differential equations, numerical treatment of integral equations, and hierarchical matrices.

Table of Contents

Part I: Linear Iterations.- Introduction.- Iterative Methods.- Classical Linear Iterations in the Positive Definite Case.- Analysis of Classical Iterations Under Special Structural Conditions.- Algebra of Linear Iterations.- Analysis of Positive Definite Iterations.- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods.- Semi-Iterative Methods.- Gradient Methods.- Conjugate Gradient Methods and Generalizations.- Part III: Special Iterations.- Multigrid Iterations.- Domain Decomposition and Subspace Methods.- H-LU Iteration.- Tensor-based Methods.- Appendices.

Editorial Reviews

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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