A VARIABLE PRECONDITIONING USING THE SOR METHOD FOR GCR-LIKE METHODS

摘要: We propose a variant of variable preconditioning for Generalized Conjugate Residual (GCR)-like methods. The is carried out by roughly solving Az = v an iterative method to certain degree accu- racy instead computing Kz in conventional preconditioned algorithm. In our proposal, the number iterations required changed at each iteration establishing stopping criterion. This enables use stationary when applying difierent precondition- ers. proposed procedure incorporated into GCR, and mathematical convergence proved. numerical experiments, we employ Successive Over-Relaxation (SOR) v, demonstrate that GCR with using SOR faster more ro- bust than incomplete LU preconditioning, FGMRES GMRESR methods General- ized Minimal (GMRES) method. Moreover, conflrm preconditioners are applied iteration.