BIT Numerical Mathematics

, Volume 35, Issue 3, pp 417–427

Entrywise relative perturbation theory for nonsingularM-matrices and applications

  • Xue Jungong
  • Jiang Erxiong

DOI: 10.1007/BF01732614

Cite this article as:
Jungong, X. & Erxiong, J. Bit Numer Math (1995) 35: 417. doi:10.1007/BF01732614


This paper establishes a new entrywise relative perturbation result for the inverse of a nonsingularM-matrixA. It is shown that a version of Gaussian elimination with one step of iterative refinement solves the systemAx =b, whereb is nonnegative, with small entrywise relative error. IfA is tridiagonal, the Gaussian elimination alone suffices.

Key words

M-matrixGaussian eliminationregular splittingiterative refinementerror analysis

Copyright information

© BIT Foundation 1995

Authors and Affiliations

  • Xue Jungong
    • 1
  • Jiang Erxiong
    • 1
  1. 1.Institute of MathematicsFudan UniversityShanghaiPeople's Republic of China