Abstract
It has been clarified by numerical experiments that a variable preconditioned GCR($m$) method using the SOR method is efficient for solving a sparse linear system. However there are cases that the residual norm of variable preconditioned GCR method stagnates. Then the inner iteration counts increase, and more computation time is required. Therefore, we propose a strategy to reduce the inner iteration counts in case of stagnation of the residual norm by using a certain parameter related to convergence behavior. Numerical experiments show that our strategy is indeed effective.
