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×n pse...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1214609 |
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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: | 2314-4785 |