Ebook: Iterative Solution of Large Sparse Systems of Equations

This book presents the description of the 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 e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.

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This book presents the description of the 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 e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.
Content:
Front Matter....Pages i-xxi
Introduction....Pages 1-11
Recapitulation of Linear Algebra....Pages 12-42
Iterative Methods....Pages 43-64
Methods of Jacobi and Gau?-Seidel and SOR Iteration in the Positive Definite Case....Pages 65-121
Analysis in the 2-Cyclic Case....Pages 122-143
Analysis for M-Matrices....Pages 144-164
Semi-Iterative Methods....Pages 165-204
Transformations, Secondary Iterations, Incomplete Triangular Decompositions....Pages 205-247
Conjugate Gradient Methods....Pages 248-295
Multi-Grid Methods....Pages 296-366
Domain Decomposition Methods....Pages 367-404
Back Matter....Pages 405-431

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This book presents the description of the 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 e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.
Content:
Front Matter....Pages i-xxi
Introduction....Pages 1-11
Recapitulation of Linear Algebra....Pages 12-42
Iterative Methods....Pages 43-64
Methods of Jacobi and Gau?-Seidel and SOR Iteration in the Positive Definite Case....Pages 65-121
Analysis in the 2-Cyclic Case....Pages 122-143
Analysis for M-Matrices....Pages 144-164
Semi-Iterative Methods....Pages 165-204
Transformations, Secondary Iterations, Incomplete Triangular Decompositions....Pages 205-247
Conjugate Gradient Methods....Pages 248-295
Multi-Grid Methods....Pages 296-366
Domain Decomposition Methods....Pages 367-404
Back Matter....Pages 405-431
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