An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation
![Thumbnail](/xmlui/bitstream/handle/10234/200024/Bader_2022_efficient.pdf.jpg?sequence=4&isAllowed=y)
View/ Open
Impact
![Google Scholar](/xmlui/themes/Mirage2/images/uji/logo_google.png)
![Microsoft Academico](/xmlui/themes/Mirage2/images/uji/logo_microsoft.png)
Metadata
Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equationDate
2022-04-30Publisher
Elsevier B.V.ISSN
0378-4754Bibliographic citation
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.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
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. [-]
Is part of
Mathematics and Computers in Simulation, Vol. 194 (april 2022)Funder Name
Ministerio de Ciencia e Innovación (MICINN) | Scientific and Technological Research Council of Turkey (TUBITAK) | EPSRC, United Kingdom
Project code
PID2019-104927GB-C21 (AEI/FEDER, UE) | TUBITAK-1059B191802292 | EP/R014604/1
Project title or grant
Método de integración geométrica para problemas cuánticos, mecánica celeste y simulacions Montecarlo I (GNI-QUAMC)mc)
Rights
© 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
This item appears in the folowing collection(s)
- MAT_Articles [765]