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＜電子ブック＞
Iterative Solution of Large Sparse Systems of Equations / by Wolfgang Hackbusch
(Applied Mathematical Sciences. ISSN:2196968X ; 95)

版	2nd ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
本文言語	英語
大きさ	XXIII, 509 p. 26 illus., 11 illus. in color : online resource
著者標目	*Hackbusch, Wolfgang author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Algebras, Linear LCSH:Differential equations FREE:Numerical Analysis FREE:Linear Algebra FREE:Differential Equations
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-28483-5

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