Some Applications for Newton-Krylov Methods with a Safeguard for GMRES(m)

Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the modified GMRES($m$), GMRESH($m$) procedure, alone and as part of an inexact Newton procedure with several choices for the forcing term, demonstrate the efficiency of the proposed strategy.