Efficient scaling and squaring method for the matrix exponential
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929320737374208 |
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| author | Blanes, Sergio Kopylov, Nikita Seydaoğlu, Muaz |
| author_facet | Blanes, Sergio Kopylov, Nikita Seydaoğlu, Muaz |
| contents | This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Padé methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then exp(A) belongs to its associated Lie group, being a property which is preserved by diagonal Padé approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12789 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient scaling and squaring method for the matrix exponential Blanes, Sergio Kopylov, Nikita Seydaoğlu, Muaz Numerical Analysis 15A16 G.1.3; G.1.7 This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Padé methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then exp(A) belongs to its associated Lie group, being a property which is preserved by diagonal Padé approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations. |
| title | Efficient scaling and squaring method for the matrix exponential |
| topic | Numerical Analysis 15A16 G.1.3; G.1.7 |
| url | https://arxiv.org/abs/2404.12789 |