谱约束下广义中心对称矩阵的最佳逼近解及扰动分析  

Best approximation solution of a generalized centrosymmetric matrix with spectra constraints and its perturbation

作　　者：谢冬秀[1] 黄宁军[2] 

机构地区：[1]北京信息科技大学理学院,北京100192 [2]北京信息科技大学学报(自然科学版)编辑部,北京100192

出　　处：《北京交通大学学报》2013年第6期139-142,共4页JOURNAL OF BEIJING JIAOTONG UNIVERSITY

基　　金：国家自然科学基金资助项目(11371075);北京市自然科学基金资助项目(1122015)

摘　　要：研究了一类广义中心对称结构的有限元模型修正的数学理论和方法.首先将模型修正问题处理为约束矩阵的最佳逼近问题,给出最佳逼近解的表达式.重点讨论了逼近解的扰动理论,并对稀疏结构的模型给出了保结构的算法.数值例子表明该方法是行之有效的.Some mathematical theories and methods are studied based on finite element analytical model updating problem of a class of generalized centrosymmetric structure. At first, the model updating problem is treated as a constraints matrix approximation problem. An expression of the best approxi- mation solution is provided. Emphasis is to establish a perturbation theory on the solution. Finally, a method is presented to preserve the sparsity of the model. The numerical examples show that the method is feasible and effective.

关 键 词：广义中心对称矩阵 矩阵范数 特征对 最佳矩阵逼近解 扰动理论 

分 类 号：O241.5[理学—计算数学]