A global variant of the COCR method for the complex symmetric Sylvester matrix equation AX + XB = C

Abstract

Complex symmetric Sylvester matrix equations appear in many applications, such as the numerical solution of the complex Helmholtz equations. In this paper, by designing a global complex symmetric M-Lanczos process we develop a global variant of the conjugate A-orthogonal conjugate residual method (Gl-COCR) for solving the Sylvester matrix equation AX+XB=C with complex symmetric coefficient matrices. To obtain the smooth and monotone convergence behavior, we also propose a smoothed Gl-COCR method, denoted by SGl-COCR. Finally, numerical examples are given to illustrate the performances of our methods.