Abstract
It has been clarified by numerical experiments that the SOR method is efficient for performing variable preconditioning when applying the Generalized Conjugate Residual (GCR) method with variable preconditioning to a sparse linear system Ax = b. However, SOR cannot be applied for solving a singular linear system, whose coefficient matrix A has zero diagonal entries or is a rectangular matrix. In this paper, we reconsider the splitting A, and propose a type of the generalized SOR (GSOR) method. Numerical experiments on singular linear systems show that the variable preconditioned GCR method combined with GSOR is significantly effective.
