Boosting the computation of the matrix exponential

•Two new Taylor algorithms for the computation of the matrix exponential are proposed.•They are based on matrix polynomial evaluation methods more efficient than Paterson–Stockmeyer method.•In tests they showed higher efficiency and accuracy than state-of-the-art Padé based methods.•They also showed...

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Vydané v:Applied mathematics and computation Ročník 340; s. 206 - 220
Hlavní autori: Sastre, J., Ibáñez, J., Defez, E.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.01.2019
Predmet:
Efficient matrix polynomial evaluation
Matrix exponential
Scaling and squaring
Taylor series
Taylor series
Efficient matrix polynomial evaluation
Scaling and squaring
Matrix exponential
ISSN:0096-3003, 1873-5649
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Shrnutí:•Two new Taylor algorithms for the computation of the matrix exponential are proposed.•They are based on matrix polynomial evaluation methods more efficient than Paterson–Stockmeyer method.•In tests they showed higher efficiency and accuracy than state-of-the-art Padé based methods.•They also showed a higher efficiency than state-of-the-art Taylor methods, and higher accuracy in some tests. This paper presents new Taylor algorithms for the computation of the matrix exponential based on recent new matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson–Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Padé algorithm for the computation of the matrix exponential, providing higher accuracy and cost performances.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.08.017