An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications
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Título
An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applicationsFecha de publicación
2009-03Editor
American Institute of PhysicsISSN
0022-2488Cita bibliográfica
CASAS, Fernando; MURUA, Ander. An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications. Journal of Mathematical Physics, 2009, vol. 50, no 3, p. 033513-1- 033513-23Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://jmp.aip.org/resource/1/jmapaq/v50/i3/p033513_s1Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
We provide a new algorithm for generating the Baker–Campbell–Hausdorff (BCH) seriesZ = log(eXeY) in an arbitrary generalized Hall basis of the free Lie algebra L(X,Y)generated by X and Y. It is based on the close ... [+]
We provide a new algorithm for generating the Baker–Campbell–Hausdorff (BCH) seriesZ = log(eXeY) in an arbitrary generalized Hall basis of the free Lie algebra L(X,Y)generated by X and Y. It is based on the close relationship of L(X,Y) with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree of 20 [111 013 independent elements in L(X,Y)] takes less than 15 min on a personal computer and requires 1.5 Gbytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when X and Y are real or complex matrices [-]
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Journal of mathematical physics, 2009, v. 50, n. 3Derechos de acceso
© 2009 American Institute of Physics
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