A Fast Solver for HSS Representations via Sparse Matrices
| Autor: | Ming Gu, W. Lyons, Shivkumar Chandrasekaran, Patrick Dewilde, T. Pals |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Rank (linear algebra)
Numerical analysis Fast multipole method MathematicsofComputing_NUMERICALANALYSIS Block matrix 010103 numerical & computational mathematics Solver 01 natural sciences 010101 applied mathematics Algebra Matrix (mathematics) Diagonal matrix 0101 mathematics Algorithm Analysis Sparse matrix Mathematics |
| Zdroj: | Siam Journal on Matrix Analysis and Applications, 29 (1) |
| ISSN: | 1095-7162 0895-4798 |
| DOI: | 10.1137/050639028 |
| Popis: | In this paper we present a fast direct solver for certain classes of dense structured linear systems that works by first converting the given dense system to a larger system of block sparse equations and then uses standard sparse direct solvers. The kind of matrix structures that we consider are induced by numerical low rank in the off-diagonal blocks of the matrix and are related to the structures exploited by the fast multipole method (FMM) of Greengard and Rokhlin. The special structure that we exploit in this paper is captured by what we term the hierarchically semiseparable (HSS) representation of a matrix. Numerical experiments indicate that the method is probably backward stable. |
| Databáze: | OpenAIRE |
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