Domain-decomposition-type methods for computing the diagonal of a matrix inverse

Jok M. Tang, Yousef Saad

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 languageEnglish (US)
Pages (from-to)2823-2847
Number of pages25
JournalSIAM Journal on Scientific Computing
Issue number5
StatePublished - 2011


  • Divide-and-conquer method
  • Domain decomposition methods
  • Iterative methods
  • Matrix diagonal extraction
  • Schur complement
  • Sherman-Morrison-Woodbury formula
  • Sparse approximate inverse


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