Iterative Solution of Large Sparse Systems of Equations / by Wolfgang Hackbusch.

Format:

Book

Author/Creator:

Hackbusch, Wolfgang., Author.

Series:

Applied Mathematical Sciences, 0066-5452 ; 95

Language:

English

Subjects (All):

Numerical analysis.

Matrix theory.

Algebra.

Differential equations, Partial.

Numerical Analysis.

Linear and Multilinear Algebras, Matrix Theory.

Partial Differential Equations.

Local Subjects:

Numerical Analysis.

Linear and Multilinear Algebras, Matrix Theory.

Partial Differential Equations.

Physical Description:

1 online resource (XXIII, 509 p. 26 illus., 11 illus. in color.)

Edition:

2nd ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

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.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-28483-5