The MGHSS for Solving Continuous Sylvester Equation AX+XB=C

Abstract

This paper proposes the modified generalization of the HSS (MGHSS) to solve a large and sparse continuous Sylvester equation, improving the efficiency and robustness. The analysis shows that the MGHSS converges to the unique solution of AX + XB = C unconditionally. We also propose an inexact variant of the MGHSS (IMGHSS) and prove its convergence under certain conditions. Numerical experiments verify the efficiency of the proposed methods.