基于谱约束的矩阵逼近解的扰动分析  

Perturbation analysis based on the best approximation solution of matrix with assigned spectra

作　　者：尹瑞娟[1] 谢冬秀[1] 

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《北京机械工业学院学报》2008年第1期9-13,共5页Journal of Beijing Institute of Machinery

基　　金：国家自然科学基金资助项目(10571012;10771022);北京市自然科学基金资助项目(1062005);北京市教学名师建设项目(61N0810810)

摘　　要：谱约束的矩阵逼近法是结构设计中模型修正的一种重要方法。给出了广义中心对称谱约束解的存在条件和一般解的表达式,对于一个预估矩阵,提供了它的逼近解的表达式,讨论了该逼近解的误差界,并且提供了一个数值方法和数值例子,数值结果表明方法可行且是有效的。The best approximation of a matrix with assigned spectra is an important method of correcting a model in the structural design. The solvability conditions for the assigned spectra of a generalized centrosymmetric matrix are established and an explicit expression of the solutions is derived. For an estimated matrix, the associated best approximation solution is deduced. Moreover, a theoretic error bound of the best solution is proposed. A numerical method is provided and an example is also carried out. Numerical examples show that the method is reliable and effective.

关 键 词：特征值问题 最佳逼近矩阵 扰动理论 

分 类 号：O241.82[理学—计算数学] O151.21[理学—数学]