The Solution Method And Theoretical Research Of Several Kinds Of Matrix Generalized Inverse Eigenvalue Problems

The generalized inverse eigenvalue problem with submatrix constraints refers to the problem that all or part of the generalized eigenvalues,the generalized eigenvectors,and the submatrix or part of the elements of the known matrix are known to construct the matrix in the matrix set satisfying certain conditions.Different types of matrix sets lead to different generalized inverse eigenvalue problems.Generalized inverse eigenvalue problems have important applications in the fields of structural design,parameter identification,principal component analysis,structural dynamics,molecular spectroscopy,vibration theory,and finite element theory.It is precisely the many different types of questions raised in these fields that have promoted the rapid development of the theory of generalized inverse eigenvalue problems,which making the generalized inverse eigenvalue problem become one of the most active and hot research topics in the field of numerical algebra today.In this paper,we mainly study several kinds of generalized inverse eigenvalue problems with structural submatrix constraints and their optimal approximation problems.These special structural matrices include generalized Hamiltonian matrix,Hermitian skew Hamiltonian matrix and Hermitian matrix.The paper is divided into four chapters.In the second chapter,the generalized inverse eigenvalue problem with submatrix constraints and the generalized Hamiltonian matrix solution of its best approximation problem are given.In the next Chapter,the Hermitian problem of its best approximation problem is given.In the last chapter,we give the Hermitian matrix solution of the generalized inverse eigenvalue problem with sub matrix constraints and its best approximation problem.In each Chapter,we raising the problem of the matrix solution at first.Secondly,taking advantage of the properties of the matrix to derive an iterative algorithm for the solution.Then,the corresponding optimal approximation solution is obtained.Finally,taking the results of numerical examples show the effectiveness of the algorithm.