Accurate computation of the smallest eigenvalue of a diagonally dominant M-matrix

Attahiru Sule Alfa, Jungong Xue, Qiang Ye

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

If each off-diagonal entry and the sum of each row of a diagonally dominant M-matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms.

Original languageEnglish
Pages (from-to)217-236
Number of pages20
JournalMathematics of Computation
Volume71
Issue number237
DOIs
StatePublished - 2002

Keywords

  • Diagonal dominant matrix
  • Eigenvalue
  • Entrywise perturbation
  • M-matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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