Polynomial approximations for the matrix logarithm with computation graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917570181857280 |
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| author | Jarlebring, Elias Sastre, Jorge González, J. Javier Ibáñez |
| author_facet | Jarlebring, Elias Sastre, Jorge González, J. Javier Ibáñez |
| contents | The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. The main computational effort lies in matrix-matrix multiplications and left matrix division. In this work we illustrate that the number of such operations can be substantially reduced, by using a graph based representation of an efficient polynomial evaluation scheme. A technique to analyze the rounding error is proposed, and backward error analysis is adapted. We provide substantial simulations illustrating competitiveness both in terms of computation time and rounding errors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial approximations for the matrix logarithm with computation graphs Jarlebring, Elias Sastre, Jorge González, J. Javier Ibáñez Numerical Analysis The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. The main computational effort lies in matrix-matrix multiplications and left matrix division. In this work we illustrate that the number of such operations can be substantially reduced, by using a graph based representation of an efficient polynomial evaluation scheme. A technique to analyze the rounding error is proposed, and backward error analysis is adapted. We provide substantial simulations illustrating competitiveness both in terms of computation time and rounding errors. |
| title | Polynomial approximations for the matrix logarithm with computation graphs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.10089 |