On Bernoulli matrix polynomials and matrix exponential approximation

We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are compared to the most efficient implementations that currently exist. For that, a state-...

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Vydáno v:Journal of computational and applied mathematics Ročník 404; s. 113207
Hlavní autoři: Defez, E., Ibáñez, J., Alonso-Jordá, P., Alonso, José M., Peinado, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.04.2022
Témata:
Bernoulli matrix approximation
GPU computing
Matrix exponential function
Matrix exponential function
Bernoulli matrix approximation
GPU computing
ISSN:0377-0427, 1879-1778
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Shrnutí:We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are compared to the most efficient implementations that currently exist. For that, a state-of-the-art test matrix battery, that allows deeply exploring the highlights and downsides of each method, has been used. Since the new algorithms proposed here do make an intensive use of matrix products, we also provide a GPUs-based implementation that allows to achieve a high performance thanks to the optimal implementation of matrix multiplication available on these devices.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2020.113207