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Iterative Solution of Large Sparse Systems of Equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Iterative Solution of Large Sparse Systems of Equations/ by Wolfgang Hackbusch.
Author:	Hackbusch, Wolfgang.
Description:	XXIII, 509 p. 26 illus., 11 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Numerical analysis. -
Online resource:	https://doi.org/10.1007/978-3-319-28483-5
ISBN:	9783319284835

Iterative Solution of Large Sparse Systems of Equations
Hackbusch, Wolfgang.

Iterative Solution of Large Sparse Systems of Equations[electronic resource] /by Wolfgang Hackbusch. - 2nd ed. 2016. - XXIII, 509 p. 26 illus., 11 illus. in color.online resource. - Applied Mathematical Sciences,95 0066-5452 ;. - Applied Mathematical Sciences,191.

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.

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.

ISBN: 9783319284835

Standard No.: 10.1007/978-3-319-28483-5doiSubjects--Topical Terms:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

Iterative Solution of Large Sparse Systems of Equations
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505 0 $a 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.
520 $a 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.
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