Abstract
We investigate the use of the multistep successive preconditioning strategies (MSP) to construct a class of parallel multilevel sparse approximate inverse (SAI) preconditioners. We do not use independent set ordering, but a diagonal dominance based matrix permutation to build a multilevel structure. The purpose of introducing multilevel structure into SAI is to enhance the robustness of SAI for solving difficult problems. Forward and backward preconditioning iteration and two Schur complement preconditioning strategies are proposed to improve the performance and to reduce the storage cost of the multilevel preconditioners. One version of the parallel multilevel SAI preconditioner based on the MSP strategy is implemented. Numerical experiments for solving a few sparse matrices on a distributed memory parallel computer are reported.
| Original language | English |
|---|---|
| Pages (from-to) | 93-106 |
| Number of pages | 14 |
| Journal | Scalable Computing |
| Volume | 7 |
| Issue number | 2 |
| State | Published - 2006 |
Bibliographical note
Publisher Copyright:© 2006 SWPS.
Funding
Kai Wang's research work was funded by the U. S. National Science Foundation under grants CCR-9902022 and ACI-0202934. Jun Zhang's research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, by the U. S. Department of Energy Office of Science under grant DE-FG02-02ER45961, by the Japanese Research Organization for Information Science & Technology, and by the University of Kentucky Research Committee. Chi Shen's research work was funded by the U.S. National Science Foundation under grants CCR-9902022 and CCR-0092532.
| Funders | Funder number |
|---|---|
| Japanese Research Organization for Information Science & Technology | |
| U. S. Department of Energy Office of Science | DE-FG02-02ER45961 |
| U. S. National Science Foundation | CCR-9902022, ACI-0202934 |
| U.S. National Science Foundation (NSF) | CCR-0092532, CCR-9988165 |
| University of Kentucky Research Committee |
Keywords
- Multilevel preconditioning
- Multistep successive preconditioning
- Parallel preconditioning
- Sparse approximate inverse
- Sparse matrices
ASJC Scopus subject areas
- General Computer Science