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＜電子ブック＞
Hierarchical Matrices : A Means to Efficiently Solve Elliptic Boundary Value Problems / by Mario Bebendorf
(Lecture Notes in Computational Science and Engineering. ISSN:21977100 ; 63)

版	1st ed. 2008.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2008
本文言語	英語
大きさ	XVI, 296 p : online resource
著者標目	*Bebendorf, Mario author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Numerical analysis LCSH:Differential equations FREE:Computational Mathematics and Numerical Analysis FREE:Numerical Analysis FREE:Differential Equations
一般注記	Low-Rank Matrices and Matrix Partitioning -- Hierarchical Matrices -- Approximation of Discrete Integral Operators -- Application to Finite Element Discretizations Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions.The theory is supported by many numerical experiments from real applications HTTP:URL=https://doi.org/10.1007/978-3-540-77147-0

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