Iterative Methods for Sparse Linear Systems: Second Edition

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SIAM, Apr 1, 2003 - Mathematics - 528 pages
3 Reviews
Tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of linear and nonlinear systems arising in typical applications has grown, meaning that using direct solvers for the three-dimensional models of these problems is no longer effective. At the same time, parallel computing, becoming less expensive and standardized, has penetrated these application areas. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. This second edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations, including a wide range of the best methods available today. A new chapter on multigrid techniques has been added, whilst material throughout has been updated, removed or shortened. Numerous exercises have been added, as well as an updated and expanded bibliography.
  

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Contents

Discretization of Partial Differential Equations
45
Sparse Matrices
73
Basic Iterative Methods
103
Projection Methods
129
Krylov Subspace Methods Part I
151
Krylov Subspace Methods Part II
217
Methods Related to the Normal Equations
245
Preconditioned Iterations
261
Preconditioning Techniques
283
Parallel Implementations
353
Parallel Preconditioners
377
Multigrid Methods
407
Domain Decomposition Methods
451
Bibliography
495
Index
517
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About the author (2003)

Yousef Saad is a College of Science and Engineering Distinguished Professor in the Department of Computer Science at the University of Minnesota. His current research interests include numerical linear algebra, sparse matrix computations, iterative methods, parallel computing, numerical methods for electronic structure and data analysis. He is a Fellow of SIAM and the AAAS.

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