Two Types Of Generalized Jacobi Matrix Inverse Eigenvalue Problems

With the rapid development of science and technology and the popularization of computer applications,Jacobi matrix inverse eigenvalue problems have been becoming more and more popular in mechanics,engineering structure design and modern mathe-matical fields and so on.In this thesis,we study the sufficient and necessary conditions and the corresponding algorithms for two types of generalized Jacobi matrix eigenvalue problems.The details are as follows:The first chapter introduces the development process of the generalized Jacobi ma-trix inverse eigenvalue problem,the main problems to be solved in the thesis and the preliminary knowledge related to this thesis,including the main reference theorems,re-lated knowledge of unitary space,some special polynomials(zero polynomial,minimal polynomial)and etc.In Chapter 2,the following problem was discussed:construct a 2n x 2n generalized Jacobi matrix such that its eigenvalues are the given complex values ?1,?2,…,?2n and its leading n×n principal submatrix is the given generalized Jacobi matrix.A sufficient and necessary condition for the solvability of the problem and an algorithm for solving this problem were obtained,a numerical example was presented to illustrate the algorithm.In Chapter 3,the following problem was discussed:for N/2?n<N,construct an N×N generalized Jacobi matrix such that the given complex values,?1,?2,…,?2N-2n,are its partial eigenvalues,and the given n×n generalized Jacobi matrix is its leading principal submatrix.A sufficient and necessary condition for the solvability of the problem and an algorithm for solving this problem were obtained,a numerical example was presented to illustrate the algorithm.