求解Lyapunov矩阵方程的梯度优化算法  

A Gradient Optimization Algorithm for Solving Lyapunov Matrix Equations

作　　者：单孟豪 唐嘉 马昌凤[1] SHAN Menghao;TANG Jia;MA Changfeng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou,Fujian 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117

出　　处：《平顶山学院学报》2024年第5期8-12,共5页Journal of Pingdingshan University

摘　　要：通过Kronecker积将Lyapunov矩阵方程的求解问题转化为优化问题,利用带有回溯的Barzilai和Borwein梯度迭代算法求解无约束最小化问题,并详细分析了其收敛性.通过数值算例说明所推导算法是有效的.In this paper,the problem of solving the Lyapunov matrix equation is mainly transformed into an optimization problem through the Kronecker product.The Barzilai and Borwein gradient iterative algorithm with backtracking is used to solve the unconstrained minimization problem.Finally,a numerical example is given to illustrate the effectiveness of the proposed algorithm.

关 键 词：LYAPUNOV矩阵方程 梯度 BBGB迭代算法 

分 类 号：O241.6[理学—计算数学]