Rank Deficiency Gradient-Based Iterations for Generalized Coupled Sylvester Matrix Equations

摘要：

　　In this paper,by constructing an objective function and using the gradient search,three gradient-based iterations are established for solving generalized coupled Sylvester matrix equations,when the related matrices are full-column rank,full-row rank or rank deficiency.It is proved that these three gradient-based iterative algorithms are convergent for any initial iterative values.By analyzing the spectral radius of the iterative matrices,we study the convergence properties and determine the optimal convergence factors of these iterations.We discuss the connection between the full-row rank iteration and the rank deficiency iteration.By using this connection,the computational efficiency increases greatly for a class of matrix equations.A numerical example is provided to illustrate the effectiveness of the proposed algorithms and testify the proposed conclusions in this paper.

关键词： Gradient-based iteration Coupled matrix equation Spectral radius Convergence analysis

作者: ZHANG Huamin DING Feng

作者单位: Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),Jiangnan University,Wuxi 214122,P.R.China

会议类型: 国际会议

会议名称: The 33th Chinese Control Conference第33届中国控制会议

会议地点: 南京

会议语种:英文

页码: 6820-6825

在线出版日期: 2014-07-28（万方平台首次上网日期，不代表论文的发表时间）