一类混合型Lyapunov矩阵方程的对称正定解  

The Symmetric Positive Definite Solution to a Class of Mixed-type Lyapunov Matrix Equations

作　　者：黄敬频[1] 

机构地区：[1]广西民族大学数学与计算机科学学院,南宁530006

出　　处：《工程数学学报》2008年第2期313-320,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10462001);广西民族大学重点科研基金(0509ZD052).

摘　　要：本文研究了一类混合型Lyapunov矩阵方程的对称正定解问题。首先将此方程转化为等价的含参矩阵方程,然后运用矩阵分解和紧凸集上不动点定理,给出了方程具有对称正定解的一些必要和充分条件:其次建立两种求方程对称正定解的参数迭代算法,分析了迭代的收敛性及参数的选取方法,并指出这两种算法的适应性和特点;数值算例表明上述算法的可行性和有效性,并对比出两种迭代的敛速。In this paper, we study the problem about the symmetric positive definite solution to a class of mixed-type Lyapunov matrix equations. By firstly transforming this equation into a matrix equation with parameter equivalently, and then applying decomposition of a matrix and a fixed point theorem on compact convex set, some necessary and sufficient conditions for the existence of a symmetric positive definite solution of this equation are derived. Next, we construct two iterative algorithms with parameter to find a symmetric positive solution of the matrix equation, the convergence of the algorithms and parameter choosing method are analyzed, and we point out the adaptability and characteristics of the two algorithms. Finally, a numerical example shows that above algorithms are feasible and efficient.

关 键 词：混合型Lyapunov矩阵方程 对称正定解 参数选取 迭代算法 

分 类 号：O151.21[理学—数学]