矩阵SR分解R因子新的扰动界  

New Perturbation Bounds for Factor R of the SR Factorization

作　　者：李平[1] 余小飞[1] LI Ping;YU Xiao-fei(Department of Fundamentals,Henan Polytechnic Institute,Nanyang 473000,China)

机构地区：[1]河南工业职业技术学院基础部

出　　处：《数学的实践与认识》2019年第23期183-190,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11701456)

摘　　要：矩阵的SR分解是求解一些优化控制问题的有效工具,如用来求解代数Riccati方程.利用分块的矩阵-向量方程方法与Lyapunov控制函数和Banach不动点定理相结合的方法获得了SR分解R因子在范数型扰动下的范数型的严格扰动界和一阶扰动界,改进了已有结果.The SR factorization is a useful tool in the computation of some optimal control problems,such as algebraic Riccati equation.In this paper,combine the block matrix-vector equation approach with the technique of Lyapunov majorant function and the Banach fixed point principle,we obtain some new rigorous perturbation bounds and first-order perturbation bound for the factor R of the SR factorization under normwise perturbations,which improved the existing results.

关 键 词：SR分解 BANACH不动点定理 严格扰动界 一阶扰动界 

分 类 号：O17[理学—数学]