一类广义Lyapunov矩阵方程的正定解  

Positive definite solution of a class of generalized Lyapunov equation

作　　者：李春梅[1] 段雪峰[1] 彭振赟[1] 江祝灵 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《纯粹数学与应用数学》2016年第5期505-514,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11561015;11301107;11261014);广西自然科学基金(2016GXNSFFA380009;2016GXNSFAA380074)

摘　　要：研究了双线性系统中的一类广义Lyapunov矩阵方程的正定解.基于混合单调算子不动点定理,给出新的存在正定解的充分条件,构造了求其正定解的不动点迭代方法,并给出了迭代误差估计公式.数值实验表明新方法是可行的.In this paper, we consider the positive definite solution of a class of generalized Lyapunov matrix equation, which arises in the bilinear systems. Based on the fixed point theorem for mixed monotone operator, a new sufficient condition for the existence of a unique positive definite solution is derived. A fixed point iterative method is proposed to compute the unique positive definite solution, and its error estimation is also given.Finally, a numerical example is presented to illustrate the feasibility of the proposed method.

关 键 词：广义Lyapunov矩阵方程 双线性系统 正定解 充分条件 迭代方法 

分 类 号：O178[理学—数学]