2024-03-29T10:19:52Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/240412021-06-10T12:56:08Zcom_10234_7037com_10234_9col_10234_8635
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Casas, Fernando
author
Murua, Ander
author
2009-03
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
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- 033513-23
0022-2488
http://hdl.handle.net/10234/24041
http://dx.doi.org/10.1063/1.3078418
Convergence
Lie algebras
Matrix algebra
Series (mathematics)
Baker–Campbell–Hausdorff series
An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications