Variant Implementations of SCBiCG Method for Linear Equations with Complex Symmetric Matrices

Abstract

SCBiCG (Bi-Conjugate Gradient method for Symmetric Complex matrices) has been proposed for solving linear equations with complex symmetric matrices, where coefficients ci need to be set by users in SCBiCG. We have had the numerical results that the residual norms of SCBiCG do not converge when the coefficients ci are real. We therefore design an efficient implementation such that the coefficients ci which are complex are given by a computation. Numerical experiments show that the residual norms of our proposed variant with the complex coefficients ci converge slightly faster than those of COCG (Conjugate Orthogonal Conjugate Gradient method) and some implementations of SCBiCG.