矩阵束最佳逼近问题的交替投影法  

Alternating projection method for matrix pencil nearness problem

作　　者：王康康[1] 戴华[1] 

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《应用数学与计算数学学报》2017年第2期163-175,共13页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11571171)

摘　　要：研究给定矩阵束的最佳逼近问题,这类问题出现在同时修正有限元模型质量矩阵和刚度矩阵的无阻尼结构系统.以矩阵束修正量的F-范数为目标函数,以待修正矩阵束应具有的性质,如满足特征方程、对称半正定性和稀疏性作为约束条件,形成带约束的矩阵束最佳逼近问题.基于交替投影方法,提出了求解矩阵束最佳逼近问题的一个数值方法.数值结果显示了新方法的有效性.In this paper, we consider the problem of finding the least change adjustment to a given matrix pencil, which arises in simultaneously correcting mass and stiffness matrices of finite element model of undamped structural systems. We impose the desired matrix properties, including satisfaction of the characteristic equation, symmetric positive semi-definiteness and sparsity, as side constraints to form the optimal matrix pencil approximation problem. Based on the alternating projection method, we present a numerical method for solving the matrix pencil nearness problem. Numerical results are presented to illustrate the performance and application of the Drooosed method.

关 键 词：交替投影法 矩阵束最佳逼近问题 模型修正 标准相关分解 

分 类 号：O241.6[理学—计算数学]