实对称五对角矩阵的两类广义特征值反问题  

Inverse generalized eigenvalue problems for two kinds of real symmetric five-diagonal matrixs

作　　者：吴静[1] 丁小丽 WU Jing;DING Xiaoli(Department of Foundation Educations,Xi’an Siyuan University,Xi’an 710038,China;College of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安思源学院基础部,西安710038 [2]西安工程大学理学院,西安710048

出　　处：《应用数学与计算数学学报》2018年第4期852-866,共15页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11501436);陕西省教育厅自然科学基金资助项目(17JK1077)

摘　　要：讨论了如下两类广义特征值反问题:(i)由给定的三个互异的特征对和给定的实对称正定五对角矩阵构造一个实对称五对角矩阵;(ii)由给定的三个互异特征对和给定的全对称正定五对角矩阵构造一个全对称五对角矩阵.利用线性方程组理论、对称向量和反对称向量的性质,分别得到了两类反问题存在唯一解的充要条件,并给出了解的表达式和数值算法;最后通过数值例子说明了算法的有效性.The following two kinds of generalized inverse eigenvalue problems are discussed in this paper:(i)a real symmetric five-diagonal matrix is constructed by the given three distinct feature pairs and one given real symmetric positive defi-nite five-diagonal matrix;(ii)a fully symmetric five-diagonal matrix is constructed by the given three distinct feature pairs and one given fully symmetric positive definite five-diagonal matrix.By using the theory of linear equations and vector nature,necessary and sufficient conditions for the existence of the unique solution for the two kinds of inverse eigenvalue problems are obtained,the expression and numerical algorithm are given.Numerical examples illustrate the effectiveness of the algorithms.

关 键 词：五对角矩阵 广义特征值 反问题 梁模型 

分 类 号：O241.6[理学—计算数学]