Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation
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Título
Computing the Matrix Exponential with an Optimized Taylor Polynomial ApproximationFecha de publicación
2019Editor
MDPIISSN
2227-7390Cita bibliográfica
BADER, Philipp; BLANES, Sergio; CASAS, Fernando. Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation. Mathematics, 2019, vol. 7, no 12, p. 1174.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.mdpi.com/2227-7390/7/12/1174Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
A new way to compute the Taylor polynomial of a matrix exponential is presented
which reduces the number of matrix multiplications in comparison with the de-facto standard
Paterson-Stockmeyer method for polynomial ... [+]
A new way to compute the Taylor polynomial of a matrix exponential is presented
which reduces the number of matrix multiplications in comparison with the de-facto standard
Paterson-Stockmeyer method for polynomial evaluation. Combined with the scaling and squaring
procedure, this reduction is sufficient to make the Taylor method superior in performance to Padé
approximants over a range of values of the matrix norms. An efficient adjustment to make the method
robust against overscaling is also introduced. Numerical experiments show the superior performance
of our method to have a similar accuracy in comparison with state-of-the-art implementations,
and thus, it is especially recommended to be used in conjunction with Lie-group and exponential
integrators where preservation of geometric properties is at issue. [-]
Publicado en
Mathematics 2019, 7, 1174.Proyecto de investigación
MTM2016-77660-P (AEI/FEDER, UE)Derechos de acceso
info:eu-repo/semantics/openAccess
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