Preconditioning techniques are widely used to speed up the convergence of iterative methods for solving large linear systems with sparse or dense coefficient matrices. For certain application problems, however, the standard block diagonal preconditioner makes the Krylov iterative methods converge more slowly or even diverge. To handle this problem, we apply diagonal shifting and stabilized singular value decomposition (SVD) to each diagonal block, which is generated from the multilevel fast multiple algorithm (MLFMA), to improve the stability and efficiency of the block diagonal preconditioner. Our experimental results show that the improved block diagonal preconditioner maintains the computational complexity of MLFMA, converges faster and also reduces the CPU cost.
|Number of pages||8|
|Journal||Applied Mathematics and Computation|
|State||Published - Nov 1 2010|
Bibliographical noteFunding Information:
This research work was supported in part by China Sichuan Higher Education Commission under grant 09ZA143 , and in part by the US National Science Foundation under grant CCF-0727600 .
- Iterative method
- Singular value decomposition (SVD)
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics