On Preconditioned Normal and Skew-Hermitian Splitting Iteration Method for Continuous Sylvester Equations AX + XB = C*

Abstract

In this paper, we present a preconditioned normal and skew-Hermitian splitting
(PNSS) iteration method for continuous Sylvester equations AX+XB =
C with positive definite/semi-definite matrices. Theoretical analysis shows
that the PNSS methods will converge unconditionally to the exact solution of
the continuous Sylvester equations. An inexact variant of the PNSS iteration
method(IPNSS) and the analysis of its convergence property in detail have
been established. Numerical experiments further show that this new method
is more efficient and robust than the existing ones.