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Titlebook: Iterative Solution of Large Sparse Systems of Equations; Wolfgang Hackbusch Book 2016Latest edition Springer International Publishing Swit

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书目名称Iterative Solution of Large Sparse Systems of Equations
编辑Wolfgang Hackbusch
视频videohttp://file.papertrans.cn/477/476591/476591.mp4
概述New edition provides emphasis on the algebraic structure of linear iteration, not usually included in most literature.Completely renewed references.Content grew out of a series of lectures given by au
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Iterative Solution of Large Sparse Systems of Equations;  Wolfgang Hackbusch Book 2016Latest edition Springer International Publishing Swit
描述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..
出版日期Book 2016Latest edition
关键词Analysis; Iterative Solution Methods; Multigrid Method; Matrices; Nonlinear Equations; Tensor-based Metho
版次2
doihttps://doi.org/10.1007/978-3-319-28483-5
isbn_softcover978-3-319-80360-9
isbn_ebook978-3-319-28483-5Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer International Publishing Switzerland 2016
The information of publication is updating

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Gradient Methodection 9.3 we discuss the drawback of the gradient directions and introduce the conjugate directions in preparation for the conjugate gradient method in the next chapter. The final Section 9.4 mentions a variant of the gradient method: the minimal residual iteration which can be applied to any regular matrix ..
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Domain Decomposition and Subspace MethodsHere we distinguish between the additive and multiplicative subspace iteration as explained in the corresponding Sections 12.6 and 12.7. Illustrations follow in Section 12.8. Interestingly, multigrid iterations can also be considered as subspace iterations as analysed in Section 12.9.
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Introductiondirect solution by the Gauss elimination is determined. This cost can be compared with the cost of the iterative methods introduced later. In Section 1.6, the Gauss–Seidel and SOR iteration are presented as first examples of linear iterations. Finally, in Section 1.7, sparsity of the underlying matrix discussed.
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-LU Iterationrrespondingly, the .-LU iteration described in Section 13.4 is very fast. The variant discussed in . 13.4.2 is purely algebraic, i.e., the data needed for the iteration are only based on the underlying matrix. Concerning details about the technique of hierarchical matrices, we refer to Appendix D.
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