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

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.