Efficient Scaling and Squaring Method for the Matrix Exponential
[EN] 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 Pade'\ methods shown to be superior in performance to the approximants used in...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:riunet______::43fb9793eda7a815e83e5a8279ccdcd8 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/234944 |
| Access Level: | acceso abierto |
| Palabra clave: | Matrix exponential Padé approximants Taylor methods Scaling and squaring Fraction decomposition Lie group |
| Sumario: | [EN] 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 Pade'\ 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 eA belongs to its associated Lie group, being a property which is preserved by diagonal Pade'\ 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. |
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