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

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 ×...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) Vol. 2024; no. 1
Main Authors: Yi, Fuxia, Li, Enhua
Format: Journal Article
Language:English
Published: Cairo John Wiley & Sons, Inc 2024
Wiley
Subjects:
Algorithms
Eigenvalues
Eigenvectors
Generalized inverse
Matrices (mathematics)
ISSN:2314-4629, 2314-4785
Online Access:Get full text
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Summary: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.
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ISSN:2314-4629
2314-4785
DOI:10.1155/2024/1214609