Generalized Inverse Eigenvalue Problem For Several Special Types Of Matrices

The problem of inverse eigenvalue of matrix has always been an important research object in numerical algebra.The problem of generalized inverse eigenvalue of pseudo-Jacobi matrix is the most common kind in the field of matrix inverse eigenvalue problem.Therefore,the study of the characteristics of the pseudo-Jacobi matrix and its spectrum is the basis for studying the problem of inverse eigenvalue.The generalized inverse characteristic value of the matrix studied in this paper is constructed according to the given part of the feature value and the corresponding eigenvectors.This paper mainly studies the inverse eigenvalue of two types of pseudo-Jacobi matrix.The full text is divided into four chapters.The first chapter introduces the background source of this paper,as well as the significance of the research and the current situation of research at home and abroad.The second chapter first studies the nature of the characteristic values of the first type of pseudo-Jacobi matrix.Then some inverse characteristic values of such pseudo-Jacobi matrix are studied.Finally,the eigenvalues and eigenvectors of such pseudo-Jacobi matrices are constructed,and prove that there is a unique solution to the problem.A numerical algorithm is obtained in the process of constructing such a pseudo-Jacobi matrix,and verified the accuracy of the algorithm.The third chapter first studies the characteristic properties of the second type of pseudo-Jacobi matrix,as well as the correlation with the characteristic values and characteristic vectors of such pseudo-Jacobi matrix,and apply mathematical inductionmethod to give proof;Then it is studied that there is a unique solution to the charge condition of the inverse characteristic value of such pseudo-Jacobi matrix;Finally,a numerical algorithm is provided to solve the problem of the inverse characteristic value of such pseudo-Jacobi matrix.And use numerical examples to illustrate the accuracy of the algorithm.The fourth chapter explains the innovation point of this paper and the prospect of future work.