Stabilizing block diagonal preconditioners for complex dense matrices in electromagnetics

Xinyu Geng, Yin Wang, Jeonghwa Lee, Jun Zhang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Pages (from-to)1983-1990
Number of pages8
JournalApplied Mathematics and Computation
Issue number5
StatePublished - Nov 1 2010

Bibliographical note

Funding 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
  • Preconditioning
  • Singular value decomposition (SVD)

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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