一类Lyapunov矩阵方程的双反对称解的迭代算法  

An Iterative Method for the Anti-bisymmetric Solution of Lyapunov Matrix Equation

作　　者：李琳[1] 袁修久[1] 李益群[1] 

机构地区：[1]空军工程大学理学院数学教研部,陕西西安710051

出　　处：《数学的实践与认识》2015年第6期273-280,共8页Mathematics in Practice and Theory

基　　金：陕西省电子信息系统综合集成重点实验室基金资助

摘　　要：基于求线性代数方程组的共轭梯度法的思想,建立一种求Lyapunov矩阵方程的双反对称解的迭代算法,对任意给定的初始双反对称矩阵,算法能够在有限步迭代计算后得到矩阵方程的极小范数双反对称解,同时在上述解集中也可得出指定矩阵的最佳逼近双反称矩阵.数值算例表明,迭代算法是有效的.On the base of conjugate gradient method of solving linear algebraic equations,.in this paper,an iterative method is presented to find the anti-bisymmetric solution of Lyapunov matrix equation.By this iterative method,for any initial anti-bisymmetric matrix,a solution can be obtained within finite iterative steps,and the solution with least-norm can be obtained by choosing a special initial matrix.In addition,the expression of its optimal approximation solution to a given matrix can be obtained.The numerical examples show that the iterative algorithm is quite efficient.

关 键 词：矩阵方程 迭代算法 极小范数解 双反对称矩阵 最佳逼近 

分 类 号：O241.6[理学—计算数学]