An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation
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Otros documentos de la autoría: Bader, Philipp; Blanes, Sergio; Casas, Fernando; Seydaoğlu, Muaz
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Título
An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equationFecha de publicación
2022-04-30Editor
Elsevier B.V.ISSN
0378-4754Cita bibliográfica
Bader, P., Blanes, S., Casas, F., & Seydaoğlu, M. (2022). An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation. Mathematics and Computers in Simulation, 194, 383-400.Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on
an efficient computation of Chebyshev polynomials of matrices and the corresponding error ... [+]
We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on
an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on Chebyshev
polynomials of degrees 2, 4, 8, 12 and 18 which are computed with only 1, 2, 3, 4 and 5 matrix–matrix products, respectively.
For problems of the form exp(−i A), with A a real and symmetric matrix, an improved version is presented that computes
the sine and cosine of A with a reduced computational cost. The theoretical analysis, supported by numerical experiments,
indicates that the new methods are more efficient than schemes based on rational Padé approximants and Taylor polynomials
for all tolerances and time interval lengths. The new procedure is particularly recommended to be used in conjunction with
exponential integrators for the numerical time integration of the Schrödinger equation. [-]
Publicado en
Mathematics and Computers in Simulation, Vol. 194 (april 2022)Entidad financiadora
Ministerio de Ciencia e Innovación (MICINN) | Scientific and Technological Research Council of Turkey (TUBITAK) | EPSRC, United Kingdom
Código del proyecto o subvención
PID2019-104927GB-C21 (AEI/FEDER, UE) | TUBITAK-1059B191802292 | EP/R014604/1
Título del proyecto o subvención
Método de integración geométrica para problemas cuánticos, mecánica celeste y simulacions Montecarlo I (GNI-QUAMC)mc)
Derechos de acceso
© 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights
reserved.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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