QR-based Parallel Set-Valued Approximation with Rational Functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913594905460736 |
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| author | Dirckx, Simon Meerbergen, Karl Huybrechs, Daan |
| author_facet | Dirckx, Simon Meerbergen, Karl Huybrechs, Daan |
| contents | In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm for scalar functions. It builds on the set-valued AAA framework introduced by Lietaert, Meerbergen, P{é}rez and Vandereycken, accelerating it by using an approximate orthogonal basis obtained from a truncated QR decomposition. We demonstrate both theoretically and numerically this method's accuracy and efficiency. We show how it can be parallelized while maintaining the desired accuracy, with minimal communication cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10260 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | QR-based Parallel Set-Valued Approximation with Rational Functions Dirckx, Simon Meerbergen, Karl Huybrechs, Daan Numerical Analysis In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm for scalar functions. It builds on the set-valued AAA framework introduced by Lietaert, Meerbergen, P{é}rez and Vandereycken, accelerating it by using an approximate orthogonal basis obtained from a truncated QR decomposition. We demonstrate both theoretically and numerically this method's accuracy and efficiency. We show how it can be parallelized while maintaining the desired accuracy, with minimal communication cost. |
| title | QR-based Parallel Set-Valued Approximation with Rational Functions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2312.10260 |