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005 2010-12-01
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101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aEfficient Numerical Methods for Non-local Operators ;$e-Matrix Compression, Algorithms and Analysis
210 3 $aEMS Press$d2010
215   $a1 online resource (441 pages)
225 1 $aEMS Tracts in Mathematics (etm)$v14$x2943-5005
330   $aHierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory.  While a dense n\times n matrix in standard representation requires n^2 units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only O(nklogn) units of storage, where k is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions and to solve matrix equations used in control theory. \mathcal{H}^2-matrices offer a refinement of hierarchical matrices: using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems.  This books gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of \mathcal{H}^2-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are only required in isolated sections, e.g., for certain classes of model problems.  Corrected 2nd printing, September 2013.
606   $aCalculus & mathematical analysis$2bicssc
606   $aNumerical analysis$2msc
615 07$aCalculus & mathematical analysis
615 07$aNumerical analysis
686   $a65-02$2msc
686   $a65F05$2msc
686   $a65N22$2msc
686   $a65N38$2msc
686   $a65R20$2msc
700   $aBörm$4aut$02012727
801  0$bDE-4084
906   $aBOOK
912   $a9910151929603321
996   $aEfficient Numerical Methods for Non-local Operators$94802852
997   $aUNINA