The analysis of restart DGMRES for solving singular linear systems

A surprising phenomenon concerning with restart DGMRES [A. Sidi, DGMRES: a GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems, Linear Algebra Appl. 335 (2001) 189–204] is presented, that small values of the restart parameter may converge faster than larger values. We take three examples where DGMRES(2) converge, while DGMRES(3) stagnates to interpret the phenomenon. Two of these examples reveals that DGMRES convergence can be extremely sensitive to small changes in the initial residual.