Abstract
This paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of specific matrices. The first uses a divide-and-conquer principle and the Sherman-Morrison-Woodbury formula and assumes that the matrix can be decomposed into a 2×2 block-diagonal matrix and a low-rank matrix. The second method is a standard domain decomposition approach in which local solves are combined with a global correction. Both methods can be successfully combined with iterative solvers and sparse approximation techniques. The efficiency of the methods usually depends on the specific implementation, which should be fine-tuned for different test problems. Preliminary results for some two-dimensional (2D) problems are reported to illustrate the proposed methods.
Original language | English (US) |
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Pages (from-to) | 2823-2847 |
Number of pages | 25 |
Journal | SIAM Journal on Scientific Computing |
Volume | 33 |
Issue number | 5 |
DOIs | |
State | Published - 2011 |
Keywords
- Divide-and-conquer method
- Domain decomposition methods
- Iterative methods
- Matrix diagonal extraction
- Schur complement
- Sherman-Morrison-Woodbury formula
- Sparse approximate inverse