A note on the iterative solutions of general coupled matrix equation

作者：Zhang, Jian-Jun^*

来源：Applied Mathematics and Computation, 2011, 217(22): 9380-9386.

DOI：10.1016/j.amc.2011.04.026

• Matrix equations
• Gradient search principle
• Krylov subspace
• Iterative
• Convergence

Recently, Ding and Chen [F. Ding, T. Chen, On iterative solutions of general coupled matrix equations, SIAM J. Control Optim. 44 (2006) 2269-2284] developed a gradient-based iterative method for solving a class of coupled Sylvester matrix equations. The basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified, so that the iterative solutions are obtained by applying hierarchical identification principle. In this note, by considering the coupled Sylvester matrix equation as a linear operator equation we give a natural way to derive this algorithm. We also propose some faster algorithms and present some numerical results.

• 出版日期2011-7-15
• 单位上海大学