Polynomial approximations for the matrix logarithm with computation graphs
[EN] 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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| 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:10251/220158 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/220158 |
| Access Level: | acceso abierto |
| Palabra clave: | Matrix logarithm Matrix square root Inverse scaling and squaring method Computation graphs Taylor series Padé approximant |
| Sumario: | [EN] 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. |
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