Rigorous Perturbation Bounds for the QX Decomposition for Centrosymmetric Matrices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916602817019904 |
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| author | Farooq, Aamir Khan, Rewayat Rani, Uzma Rahim, M. Tariq |
| author_facet | Farooq, Aamir Khan, Rewayat Rani, Uzma Rahim, M. Tariq |
| contents | Konrad Burnik suggests a structure-preserving QR factorization for centrosymmetric matrices, known as QX factorization. In this article, we obtain the explicit expressions for rigorous perturbation bounds of the QX factorization when the original matrix is perturbed, either norm-wise or component-wise. First, using the matrix-equation approach, weak rigorous perturbation bounds are derived. Then, strong rigorous perturbation bounds are obtained by combining the modified matrix-vector equation approach with the strategy for the Lyapunov majorant function and the Banach fixed-point theorem. The mixed and component-wise condition numbers and their upper bounds are also explicitly expressed. Numerical tests illustrate the validity of the obtained results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_04698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigorous Perturbation Bounds for the QX Decomposition for Centrosymmetric Matrices Farooq, Aamir Khan, Rewayat Rani, Uzma Rahim, M. Tariq Numerical Analysis Functional Analysis 15A23, 15A45 Konrad Burnik suggests a structure-preserving QR factorization for centrosymmetric matrices, known as QX factorization. In this article, we obtain the explicit expressions for rigorous perturbation bounds of the QX factorization when the original matrix is perturbed, either norm-wise or component-wise. First, using the matrix-equation approach, weak rigorous perturbation bounds are derived. Then, strong rigorous perturbation bounds are obtained by combining the modified matrix-vector equation approach with the strategy for the Lyapunov majorant function and the Banach fixed-point theorem. The mixed and component-wise condition numbers and their upper bounds are also explicitly expressed. Numerical tests illustrate the validity of the obtained results. |
| title | Rigorous Perturbation Bounds for the QX Decomposition for Centrosymmetric Matrices |
| topic | Numerical Analysis Functional Analysis 15A23, 15A45 |
| url | https://arxiv.org/abs/2502.04698 |