Breakdown-free gmres for singular systems

Lothar Reichel, Qiang Ye

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsingular matrix. When the matrix is singular, GMRES may break down before an acceptable approximate solution has been determined. This paper discusses properties of GMRES solutions at breakdown and presents a modification of GMRES to overcome the breakdown.

Original languageEnglish
Pages (from-to)1001-1021
Number of pages21
JournalSIAM Journal on Matrix Analysis and Applications
Issue number4
StatePublished - 2005


  • Iterative method
  • Krylov subspace
  • Linear system
  • Singular matrix

ASJC Scopus subject areas

  • Analysis


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