Hierarchical matrices : a means to efficiently solve elliptic boundary value problems
著者
書誌事項
Hierarchical matrices : a means to efficiently solve elliptic boundary value problems
（Lecture notes in computational science and engineering, 63）
Springer, c2008
- : [pbk.]
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注記
Includes bibliographical reference (p. 269-279) and index
"With 45 Figures and 53 Tables"
内容説明・目次
内容説明
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.
目次
Low-Rank Matrices and Matrix Partitioning.- Hierarchical Matrices.- Approximation of Discrete Integral Operators.- Application to Finite Element Discretizations.
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