Breakdown-free GMRES for Singular Systems
Lothar Reichel, Qiang John Ye · SIAM Journal on Matrix Analysis and Applications · 2005
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.