Name
Abstract | ||
|---|---|---|
Sparse approximate inverses are considered as smoothers for multigrid. They are based on the SPAI-Algorithm [M. J. Grote and T. Huckle, SIAM J. Sci. Comput., 18 (1997), pp. 838--853], which constructs a sparse approximate inverse M of a matrix A by minimizing I -MA in the Frobenius norm. This yields a new hierarchy of smoothers: SPAI-0, SPAI-1, SPAI$(\varepsilon)$. Advantages of SPAI smoothers over classical smoothers are inherent parallelism, possible local adaptivity, and improved robustness. The simplest smoother, SPAI-0, is based on a diagonal matrix M. It is shown to satisfy the smoothing property for symmetric positive definite problems. Numerical experiments show that SPAI-0 smoothing is usually preferable to damped Jacobi smoothing. For the SPAI-1 smoother the sparsity pattern of M is that of A; its performance is typically comparable to that of Gauss--Seidel smoothing; however, both the computation and the application of the smoother remain inherently parallel. In more difficult situations, where the simpler SPAI-0 and SPAI-1 smoothers are not adequate, the SPAI$(\varepsilon)$ smoother provides a natural procedure for improvement where needed. Numerical examples illustrate the usefulness of SPAI smoothing. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1137/S1064827500380623 | SIAM Journal on Scientific Computing |
Keywords | Field | DocType |
multilevel methods,approximate inverses,smoothing property,parallel preconditioning,iterative methods,sparse linear systems | Mathematical optimization,Matrix (mathematics),Iterative method,Positive-definite matrix,Matrix norm,Smoothing,Diagonal matrix,Multigrid method,Sparse matrix,Mathematics | Journal |
Volume | Issue | ISSN |
23 | 4 | 1064-8275 |
Citations | PageRank | References |
11 | 1.00 | 13 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Oliver Bröker | 1 | 11 | 1.00 |
| Marcus J. Grote | 2 | 401 | 51.61 |
| Carsten Mayer | 3 | 11 | 1.00 |
| Arnold Reusken | 4 | 305 | 44.91 |