A New Circulant Preconditioned GMRES Method for Solving Ordinary Differential Equation

摘要

The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods.In this paper,we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method,which is a convex linear combination of P-circulant and Strang-type circulant preconditioners.Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases.