The Computational Solution of Generalized Inverse Eigenvalue Problem for Pseudo‐Jacobi Matrix

Abstract

This paper is concerned with two generalized inverse eigenvalue problems for a kind of pseudo‐Jacobi matrix. From a non‐Hermite matrix, an r × r Jacobi matrix, two distinct real eigenvalues, and part of the corresponding eigenvectors, an n × n pseudo‐Jacobi matrix is constructed. Furthermore, an n × n pseudo‐Jacobi matrix can be made by two different eigenpairs and a positive definite diagonal matrix. It is shown that a unique pseudo‐Jacobi matrix can be recovered from partial eigenpairs and certain special mixed eigendata. Two algorithms are provided for the reconstruction of such a pseudo‐Jacobi matrix, and illustrative numerical examples are presented to verify the proposed algorithms.