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

Edition	1st ed. 2008.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2008
Language	English
Size	XVI, 296 p : online resource
Authors	*Bebendorf, Mario author SpringerLink (Online service)
Subjects	LCSH:Mathematics -- Data processing  All Subject Search LCSH:Numerical analysis LCSH:Differential equations FREE:Computational Mathematics and Numerical Analysis FREE:Numerical Analysis FREE:Differential Equations
Notes	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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