Abstract:

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.

Key words: Periodic Jacobi matrix, Spectral distribution, Reconstruction algorithm, Inverse eigenvalue problem