Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/050639028 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
hierarchically semiseparable representations,dense structured linear system,block sparse equation,hss representations,low-rank structures,standard sparse direct solvers,larger system,sparse matrices,dense system,fast solvers,orthogonal factorizations,numerical experiment,numerical low rank,fast multipole method,fast direct solver,direct sparse solvers,fast solver,matrix structure,rank,linear system,factorisation,linear algebra,diagonal matrix,numerical method,block matrix,factorization,numerical analysis | Linear algebra,Algebra,Mathematical analysis,Matrix (mathematics),Algorithm,Fast multipole method,Solver,Numerical analysis,Diagonal matrix,Block matrix,Sparse matrix,Mathematics | Journal |
Volume | Issue | ISSN |
29 | 1 | 0895-4798 |
Citations | PageRank | References |
35 | 1.59 | 4 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Chandrasekaran | 1 | 318 | 36.99 |
| P. Dewilde | 2 | 88 | 6.00 |
| M. Gu | 3 | 343 | 38.91 |
| W. Lyons | 4 | 35 | 1.59 |
| T. Pals | 5 | 35 | 1.59 |