一类周期伪Jacobi矩阵的逆特征值问题

An Inverse Eigenvalue Problem for a Kind of Periodic Pseudo-Jacobi Matrix

该文考虑了一类周期伪Jacobi矩阵的逆特征值问题,该矩阵依赖于一个符号算子,该符号算子分量的变化将会对整个矩阵的谱造成很大的扰动.于是根据该矩阵特征方程根的分布情况来讨论其特征值的分布.当该符号算子中最后一个分量发生变化时,给出了其逆特征值问题可解的充要条件和具体的构造过程.最后,通过数值算例验证了所给算法的有效性和可行性.

In this paper,we consider the inverse eigenvalue problem of a class of periodic pseudo-Jacobi matrices,relying on a signature operator,whose component changes will cause large perturbations to the entire spectra of these matrices.The distribution of their eigenvalues is firstly discussed according to the roots distribution of the secular equations of these matrices.When the last component of the signature operator changes,the necessary and sufficient conditions for the solvability of the inverse eigenvalue problem are given,and the concrete construction process is also presented.Numerical examples are finally given to verify the effectiveness and feasibility of the proposed algorithm.