A new rational approximation algorithm via the empirical interpolation method
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912198826131456 |
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| author | Li, Aidi Li, Yuwen |
| author_facet | Li, Aidi Li, Yuwen |
| contents | We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for space-fractional differential equations, parameter-robust preconditioning, and evaluation of matrix functions. Compared to classical rational approximation algorithms, the proposed method is more efficient for approximating a large number of target functions. In addition, we derive a convergence estimate of our rational approximation algorithm using the metric entropy numbers. Numerical experiments are included to demonstrate the effectiveness of the proposed method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_19339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new rational approximation algorithm via the empirical interpolation method Li, Aidi Li, Yuwen Numerical Analysis We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for space-fractional differential equations, parameter-robust preconditioning, and evaluation of matrix functions. Compared to classical rational approximation algorithms, the proposed method is more efficient for approximating a large number of target functions. In addition, we derive a convergence estimate of our rational approximation algorithm using the metric entropy numbers. Numerical experiments are included to demonstrate the effectiveness of the proposed method. |
| title | A new rational approximation algorithm via the empirical interpolation method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.19339 |