Iterative Solution of Large Sparse Systems of Equations: v.95 (Applied Mathematical Sciences) - Hardcover

Hackbusch, Wolfgang

Hardcover

ISBN 10: 3540940642 ISBN 13: 9783540940647

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1993

Synopsis

This text presents a description of the current 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 the additive and multiplicative Schwartz method). All techniques are described algebraically, and each is illustrated by a PASCAL program applicable to a class of model problems.

About this title

From the Back Cover

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.

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.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1993
• Language: English
• ISBN 10: 3540940642
• ISBN 13: 9783540940647
• Binding: Hardcover
• Number of pages: 450