A shift-splitting hierarchical identification method for solving Lyapunov matrix equations

作者：Gu Chuanqing^*; Xue Huiyan

来源：Linear Algebra and Its Applications, 2009, 430(5-6): 1517-1530.

DOI：10.1016/j.laa.2008.01.010

• Matrix equations
• Hierarchical identification principle
• Shift-splitting
• Iterative method

In the present paper, we propose a hierarchical identification method (SSHI) for solving Lyapunov matrix equations, which is based on the symmetry and skew-symmetry splitting of the coefficient matrix. We prove that the iterative algorithm consistently converges to the true solution for any initial values with some conditions, and illustrate that the rate of convergence of the iterative solution can be enhanced by choosing the convergence factors appropriately. Furthermore, we show that the method adopted can be easily extended to study iterative solutions of other matrix equations, such as Sylvester matrix equations. Finally, we test the algorithms and show their effectiveness using numerical examples.

• 出版日期2009-3-1
• 单位上海大学