| The problem of inverse eigenvalue of Jacobi matrix has always been an important research object by scholars at home and abroad.With the development of science and technology,the inverse eigenvalue problem of the Jacobi matrix has been widely used in vibration equations,aerodynamics and other fields.On this basis,this paper studies the inverse eigenvalue problems of two types of special matrices,one is pseudo-Jacobi matrix,and the other is sub-period Jacobi matrix.This paper studied a special kind of pseudo Jacobi matrix.Firstly,we analyzed the spectral properties of such matrices,discussed the existence theorems of such matrices in two cases,and found the number of solutions in the corresponding cases.Later,we proposed a method of reconstructing the matrix from three sets of spectral data.And finally a specific numerical example to proved the effectiveness of the algorithm.At the same time,we discusseed the inverse eigenvalue problem of a class of sub-periodic Jacobi matrices.First,the spectral properties of the sub-period Jacobi matrix are studied.Secondly,the necessary and sufficient conditions for such a matrix to have a solution and a unique solution are given in two cases,and an algorithm for re-constructing the sub-period Jacobi matrix is proposed.In the end,there is a specific numerical example to prove the effectiveness of the algorithm. |
