The Inverse Generalized Eigenvalue Problem For Generalized Jacobi Matrices

The Inverse eigenvalue problem for matrices in the problems involved in the field of mathematical physics, geophysics, quantum chemistry, optics, mechanics, structural design, pattern recognition, automatic control, and so on. Many experts and scholars have addressed this problem more extensively and in-depth studied, and get a lot of results. Some have been used in engineering or scientific calculations of practical solutions. this paper mainly presents the inverse generalized eigenvalue problem for generalized Jacobi matrices and generalized inverse eigenvalue problem for periodic jacobi matrices, which are described as follows:In the first part, we discuss the background of the inverse eigenvalue problems for matrices and introduce the structure of this paper, the specific contents include from the inverse eigenvalue problems for matrices,the inverse eigenvalue problems for Jacobi matrices to the inverse generalized eigenvalue problem which is the core of this paper, we introuce the background and advances of the inverse problems.The second part is the central of this dissertation, it describes inverse generalized eigenvalue problem, which includes inverse generalized eigenvalue problem for generalized Jacobi matrices,inverse generalized eigenvalue problem for generalized acobi matrices with linear relation and inverse generalized eigenvalue problem for principal square submatrix. Discussing the necessary and sufficient conditions of the problems which have a unique solution, the expression of the solution of the problem is given, some numerical example is provided.The third part is also the central of this dissertation, it describes the generalized inverse eigenvalue problem for generalized periodic Jacobi matrices, we discuss the only existing conditions of the solution for the generalized inverse eigenvalue problem of generalized three-diagonal matrices,generalized five-diagonal matrices, Using matlab]to operate the results, finally we get the desired results.