Breakdown-free GMRES for Singular Systems

Abstract

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.

DOI: 10.1137/S0895479803437803

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Cite this paper

@article{Reichel2005BreakdownfreeGF, title={Breakdown-free GMRES for Singular Systems}, author={Lothar Reichel and Qiang Ye}, journal={SIAM J. Matrix Analysis Applications}, year={2005}, volume={26}, pages={1001-1021} }