New scaling-squaring Taylor algorithms for computing the matrix exponential
The matrix exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the matrix exponential is a combination of “scaling and squaring” with a Pad´e app...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/63733 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/63733 |
| Access Level: | acceso abierto |
| Palabra clave: | Matrix exponential Taylor series Paterson--Stockmeyer method Backward error analysis Computational cost analysis CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL MATEMATICA APLICADA LENGUAJES Y SISTEMAS INFORMATICOS TEORIA DE LA SEÑAL Y COMUNICACIONES |
| Sumario: | The matrix exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the matrix exponential is a combination of “scaling and squaring” with a Pad´e approximation. For alternative scaling and squaring methods based on Taylor series, we present two modifications that provably reduce the number of matrix multiplications needed to satisfy the required accuracy bounds, and a detailed comparison of the several algorithmic variants is provided. |
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