Inverse Eigenvalue Problem For Generalized Periodic Jacobi Matrices

Algebra inverse eigenvalue problem is how to used the all or part of the known eigenvalue or eigenvalue vectors to construct matrix to meet the requirements under the conditions of the relevant constraints or specify the matrices. Algebra inverse eigenvalue problem in structural design, parameter identification, principal component analysis, surveying, remote sensing, biology, electronics, optics, solid mechanics, structural dynamics, molecular spectroscopy, automatic control theory, vibration theory, cyclical theory, line planning and non-linear planning theory, finite element theory and other fields has important applications. Inverse eigenvalue problem for generalized periodic Jacobi matrices not only has high academic value, but also has broad application prospects.This article describes the concepts, theories related to the issues, and has done a thorough study and elaborated of the generalized periodic Jacobi matrix inverse eigenvalue problems. In the fully absorb and digest foreign scholars on the matrix inverse eigenvalue problems based on the results of research, gets the following three parts of the main elements:The first part describes the current algebra inverse eigenvalue problem of the progress has been made in the study, a kind of the inverse eigenvalue problem for tridiagonal matrix has a unique solution of the necessary and sufficient conditions for the expression of reconciliation, the conditions of the solution for the inverse eigenvalue problem for tridiagonal matrices with linear relation is only exist, as well as the sufficient conditions of the inverse eigenvalue problem for real symmetric seven-diagonal matrix for solvability of the expression of reconciliation. The conclusions, the theorems and the numerical examples are given to checking.The second part describes the inverse eigenvalue problem for Jacobi matrices and has achieved research results, discusses the existence conditions of the inverse eigenvalue problem for generalized Jacobi matrices , the necessary and sufficient conditions of the characteristics of group inverse problems generalized Jacobi matrix inverse eigenvalue problem have a unique solution , as well as the existence and uniqueness conditions of the inverse eigenvalue problem for generalized Jacobi matrice. Numerical examples are given to checking.The third part is the main part of this paper. First introduced a class of inverse eigenvalue problems for generalized periodic Jacobi matrix, and theorems and numerical examples are given. Then put forward for an algorithm for solving inverse eigenproblem of generalized periodic Jacobi Matrices. Finally, introduced the inverse eigenvalue problem for generalized periodic Jacobi matrices with linear relation.The third part is the main part of this paper. This chapter describes the only existence conditions of a class of inverse eigenvalue problem for generalized periodic Jacobi matrix. put forward for an algorithm for solving inverse eigenproblem of generalized periodic Jacobi Matrices. Finally, the only existing conditions of the solution for the inverse eigenvalue problem for generalized periodic Jacobi matrices with linear relation are discussed. Numerical examples are given to checking.