一类五对角矩阵的特征值反问题及应用  

Inverse eigenvalue problems and applications for a kind of real five-diagonal matrix

作　　者：吴静[1] 丁小丽 

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

出　　处：《纺织高校基础科学学报》2017年第3期429-437,共9页Basic Sciences Journal of Textile Universities

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(2016JK2150)

摘　　要：通过建立广义雅可比矩阵与五对角矩阵的关系,用3个互异的特征对和2个互异的特征对及n-2个实数分别构造非对称五对角矩阵的特征值反问题,并给出这两类问题有解的存在性和唯一的充分与必要条件.将所得结论应用于梁系结构,将梁模型转化为一类特殊的非对称五对角矩阵的特征值反问题,构造算法并通过数值计算解决了这两类反问题.By establishing the relationship of generalized Jacobi matrix and the 5-diagonal matrix,two kinds of inverse eigenvalue problems consisting of three different eigen-pairs,two different eigen-pairs and n-2real numbers are proposed to construct a dissymmetric 5-diagonal matrix.And the sufficient and necessary conditions for the existence and uniqueness of the solutions are also obtained.By applying the result to the beam system,and the beam modelis is transformed into a class of inverse eigenvalue problems of a special dissymmetric 5-diagonal matrix,by constructing algorithm,two kinds of inverse problems are solved by numerical calculation.

关 键 词：五对角矩阵 雅可比矩阵 反问题 梁模型 

分 类 号：O241.6[理学—计算数学]