BREAKDOWNS OF RRGMRES and DGMRES

The GMRES method is one of the most common iterative methods to solve linearsystems of equations with an n × n large nonsingular matrix . When the matrix issingular, the GMRES method may break down before determining an acceptable approximatesolution. The RRGMRES and DGMRES are modified GMRES restrictingthe Krylov subspaces within the range of A and the range of Am to make solutionsmore stable, where m is the index of A. The aim of this paper is to characterizebreakdowns and least square solutions of the RRGMRES and DGMRES algorithmsfor solving a singular linear system equations.