IRKA is a Riemannian Gradient Descent Method
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911949887897600 |
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| author | Mlinarić, Petar Beattie, Christopher A. Drmač, Zlatko Gugercin, Serkan |
| author_facet | Mlinarić, Petar Beattie, Christopher A. Drmač, Zlatko Gugercin, Serkan |
| contents | The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the $\mathcal{H}_2$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixed step size over the manifold of rational functions having fixed degree. This interpretation motivates the development of a Riemannian gradient descent method utilizing as a natural extension variable step size and line search. Comparisons made between IRKA and this extension on a few examples demonstrate significant benefits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02031 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | IRKA is a Riemannian Gradient Descent Method Mlinarić, Petar Beattie, Christopher A. Drmač, Zlatko Gugercin, Serkan Numerical Analysis Systems and Control Optimization and Control The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the $\mathcal{H}_2$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixed step size over the manifold of rational functions having fixed degree. This interpretation motivates the development of a Riemannian gradient descent method utilizing as a natural extension variable step size and line search. Comparisons made between IRKA and this extension on a few examples demonstrate significant benefits. |
| title | IRKA is a Riemannian Gradient Descent Method |
| topic | Numerical Analysis Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2311.02031 |