Iterative Solution of Large Sparse Systems of Equations

✍ Scribed by Wolfgang Hackbusch (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 528
• Series: Applied Mathematical Sciences 95
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxiii
Front Matter....Pages 1-2
Introduction....Pages 3-16
Iterative Methods....Pages 17-34
Classical Linear Iterations in the Positive Definite Case....Pages 35-67
Analysis of Classical Iterations Under Special Structural Conditions....Pages 69-88
Algebra of Linear Iterations....Pages 89-122
Analysis of Positive Definite Iterations....Pages 123-136
Genenration of Iterations....Pages 137-172
Front Matter....Pages 173-174
Semi-Iterative Methods....Pages 175-209
Gradient Method....Pages 211-228
Conjugate Gradient Methods and Generalisations....Pages 229-262
Front Matter....Pages 263-264
Multigrid Iterations....Pages 265-324
Domain Decomposition and Subspace Methods....Pages 325-370
(\mathcal {H}) -LU Iteration....Pages 371-384
Tensor-based Methods....Pages 385-400
Back Matter....Pages 401-509

✦ Subjects

Numerical Analysis; Linear and Multilinear Algebras, Matrix Theory; Partial Differential Equations