Solving Sylvester equation with complex symmetric semi-definite positive coefficient matrices

Abstract

Combination of real and imaginary parts (CRI) works well for solving complex symmetric linear systems. This paper develops a generalization of CRI method to determine the solution of Sylvester matrix equation. We show that this, regardless of condition, converges to solution of the Sylvester equation. At the end we test the new scheme by solving a numerical example.

An efficient method for solving non-negative Sylvester matrix equations

“…Besides, [7] introduced some convergence results of the gradient-based iterative algorithm and [8] gave an extended Krylov subspace method for solving AX XB C   . A generalized combination of real and imaginary parts (CRI) is considered when coefficient matrices are complex symmetric semi-definite positive in [9]. Moreover, Alternating Direction Method of Multipliers (ADMM) is widely used to solve convex and nonconvex problems, see [10] for example.…”