A New Method for Computing the Diagonal of a Matrix Inverse

Tang Jok Man, Yousef Saad

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The computation of some entries of a matrix inverse arises in several important applications in practice. This paper presents a probing method for determining the diagonal of the inverse of a sparse matrix in the common situation when its inverse exhibits a decay property. A few simple properties of the inverse suggest a way to determine effective probing vectors based on standard graph theory results. An iterative method is then applied to solve the resulting sequence of linear systems, from which the diagonal of the matrix inverse is extracted. Results of numerical experiments are provided to demonstrate the effectiveness of the proposed method.

Original languageEnglish (US)
Pages (from-to)69-72
Number of pages4
JournalHKIE Transactions Hong Kong Institution of Engineers
Volume17
Issue number4
DOIs
StatePublished - Jan 1 2010

Keywords

  • Covariance Matrices
  • Graph Theory
  • Green’s Functions
  • Krylov-subspace Methods
  • Matrix Diagonal Extraction
  • Probing
  • Sparse Approximate Inverses

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