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.
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)
