A Global Transpose-Free Method With Quasi-Minimal Residual Strategy for the Sylvester Equations

Ke Zhang, Chuanqing Gu

The Sylvester equation has numerous applications in control and system theory, power system, linear algebra, model reduction and signal processing. In the present paper, a global transpose-free quasi-minimal residual method for the Sylvester equations is proposed. The resulting method, with short-term recurrences, does not involve the multiplication with the transpose of the coefficient matrices, and often exhibits smoother convergence behavior than some other existing global methods. Finally, several numerical examples are reported by comparing the proposed method with some global methods.