準残差の最小化に基づくBiCGSafe法の収束性について

抄録

The Bi-Conjugate Gradient method or Lanczos algorithm is an important guideline of a generalized CG method. In particular, BiCGStab method is among well known methods for solving a linear system of equations with unsymmetric coefficient matrix. However, the occurrence of breakdown of the methods can cause failure to converge to the solution. In this paper we present algorithm of new product-type BiCG method based on the minimization of an associate residual vector in place of the residual vector. Numerical experiments show safe convergence of the proposed BiCGSafe method as compared with the existing GPBi-CG and BiCGStab methods.