Eigenvalue inverse problem for generalized Jacobi matrices with periodic plus edges

Abstract

In this paper, the eigenvalue inverse problem for generalized Jacobi matrices with period plus edges is studied, and such problems have some applications in research in the fields of mathematics, engineering, quantum mechanics, and other disciplines. A row-by-row inversion of the nonzero elements of the matrix is carried out with the given two eigenpairs, and several lemmas are formed by discussing the cases during the inversion process, which in turn gives the solution of this inverse problem, and the corresponding existence uniqueness theorem of the solution is obtained. And two numerical examples are used for checking and achieving the expected results.