Block diagonalization of (p, q)-tridiagonal matrices
In this article, we study the block diagonalization of (p,q)\left(p,q)-tridiagonal matrices and derive closed-form expressions for the number and structure of diagonal blocks as functions of the parameters pp, qq, and nn. This reduction enables efficient computation of eigenvalues and eigenvectors b...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-08-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2025-0041 |
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| Summary: | In this article, we study the block diagonalization of (p,q)\left(p,q)-tridiagonal matrices and derive closed-form expressions for the number and structure of diagonal blocks as functions of the parameters pp, qq, and nn. This reduction enables efficient computation of eigenvalues and eigenvectors by decomposing the matrix into smaller subproblems. We extend the method to more general (P,Q)\left({\mathcal{P}},{\mathcal{Q}})-tridiagonal matrices, where P{\mathcal{P}} and Q{\mathcal{Q}} are sets of positive integers, covering general banded structures. We also examine special cases such as bidiagonal and triangular block reductions along with supporting algorithms and numerical examples. |
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| ISSN: | 2300-7451 |