Model Order Reduction for Parametric Hermitian Eigenvalue Problems: Local Acceleration with Taylor-Reduced Basis Method
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910079215730688 |
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| author | Stamm, Benjamin Zeng, Zhuoyao |
| author_facet | Stamm, Benjamin Zeng, Zhuoyao |
| contents | This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs an approximation space by capturing derivatives information of the spectral projector at a reference point in the parameter domain. We perform a concise error analysis to justify the Taylor-RBM for eigenvalue problems, and we present a computationally efficient procedure to assemble the Taylor-reduced basis space. Since this method is tightly connected to the classical multivariate analytic perturbation theory, we also provide a detailed analysis of the spectral approximation using the truncated power series of the eigenprojector, and compare this with the approximation obtained from the Taylor-RBM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14620 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Model Order Reduction for Parametric Hermitian Eigenvalue Problems: Local Acceleration with Taylor-Reduced Basis Method Stamm, Benjamin Zeng, Zhuoyao Numerical Analysis Primary 41A63, 65F15, secondary 47A55, 65N25, 65F50, 65K10, 81P68 This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs an approximation space by capturing derivatives information of the spectral projector at a reference point in the parameter domain. We perform a concise error analysis to justify the Taylor-RBM for eigenvalue problems, and we present a computationally efficient procedure to assemble the Taylor-reduced basis space. Since this method is tightly connected to the classical multivariate analytic perturbation theory, we also provide a detailed analysis of the spectral approximation using the truncated power series of the eigenprojector, and compare this with the approximation obtained from the Taylor-RBM. |
| title | Model Order Reduction for Parametric Hermitian Eigenvalue Problems: Local Acceleration with Taylor-Reduced Basis Method |
| topic | Numerical Analysis Primary 41A63, 65F15, secondary 47A55, 65N25, 65F50, 65K10, 81P68 |
| url | https://arxiv.org/abs/2603.14620 |