Generalized inverse eigenvalue problems for augmented periodic Jacobi Matrices

Abstract

In this paper, we propose a new method to solve the generalized inverse eigenvalue problem for periodic Jacobi matrices. Besides, we introduce a new inverse eigenvalue problem for augmented periodic Jacobi matrices, and present a corresponding stable algorithm to solve this inverse problem. Numerical experiments show that the new method we proposed is efficient.

Newton‐like and inexact Newton‐like methods for a parameterized generalized inverse eigenvalue problem

“…There are various forms of the inverse eigenvalue problem that appear depending on the applications; for several forms, one may refer to other studies 1‐9 . Generally, in all the inverse eigenvalue problems, the given information contains either all or part of the eigenvalues or eigenvectors, and the unknown parameters are the elements of a matrix or a matrix pencil 1 .…”

“…There are various forms of the inverse eigenvalue problem that appear depending on the applications; for several forms, one may refer to other studies. [1][2][3][4][5][6][7][8][9] Generally, in all the inverse eigenvalue problems, the given information contains either all or part of the eigenvalues or eigenvectors, and the unknown parameters are the elements of a matrix or a matrix pencil. 1 In this paper, we study a kind of inverse eigenvalue problem that appears in many practical applications in areas such as structural engineering, mechanics, and physics.…”