Randomized sketching of nonlinear eigenvalue problems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929399593435136 |
|---|---|
| author | Güttel, Stefan Kressner, Daniel Vandereycken, Bart |
| author_facet | Güttel, Stefan Kressner, Daniel Vandereycken, Bart |
| contents | Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such approximants numerically. For large-scale vector- and matrix-valued functions, however, the direct application of the set-valued variant of AAA becomes inefficient. We propose and analyze a new sketching approach for such functions called sketchAAA that, with high probability, leads to much better approximants than previously suggested approaches while retaining efficiency. The sketching approach works in a black-box fashion where only evaluations of the nonlinear function at sampling points are needed. Numerical tests with nonlinear eigenvalue problems illustrate the efficacy of our approach, with speedups above 200 for sampling large-scale black-box functions without sacrificing on accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12175 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Randomized sketching of nonlinear eigenvalue problems Güttel, Stefan Kressner, Daniel Vandereycken, Bart Numerical Analysis 65H17 (Primary), 68W20 (Secondary), 41A20, 30E10, 65F50 Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such approximants numerically. For large-scale vector- and matrix-valued functions, however, the direct application of the set-valued variant of AAA becomes inefficient. We propose and analyze a new sketching approach for such functions called sketchAAA that, with high probability, leads to much better approximants than previously suggested approaches while retaining efficiency. The sketching approach works in a black-box fashion where only evaluations of the nonlinear function at sampling points are needed. Numerical tests with nonlinear eigenvalue problems illustrate the efficacy of our approach, with speedups above 200 for sampling large-scale black-box functions without sacrificing on accuracy. |
| title | Randomized sketching of nonlinear eigenvalue problems |
| topic | Numerical Analysis 65H17 (Primary), 68W20 (Secondary), 41A20, 30E10, 65F50 |
| url | https://arxiv.org/abs/2211.12175 |