An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications TeX Export

@article{citeulike:3420788, abstract = {We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series \$Z = \log(\e^X \e^Y)\$ in an arbitrary generalized Hall basis of the free Lie algebra \$\mathcal{L}(X,Y)\$ generated by \$X\$ and \$Y\$. It is based on the close relationship of \$\mathcal{L}(X,Y)\$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in \$\mathcal{L}(X,Y)\$) takes less than 15 minutes 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.}, archivePrefix = {arXiv}, author = {Casas, Fernando and Murua, Ander}, citeulike-article-id = {3420788}, citeulike-linkout-0 = {http://arxiv.org/abs/0810.2656}, citeulike-linkout-1 = {http://arxiv.org/pdf/0810.2656}, eprint = {0810.2656}, keywords = {algorithms, computation, mathematics, printed, quantum}, month = {Oct}, posted-at = {2009-06-01 21:31:42}, priority = {3}, title = {An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications}, url = {http://arxiv.org/abs/0810.2656}, year = {2008} }

TY - JOUR ID - citeulike:3420788 L3 - citeulike-article-id:3420788 N2 - We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series $Z = \log(\e^X \e^Y)$ in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$. It is based on the close relationship of $\mathcal{L}(X,Y)$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in $\mathcal{L}(X,Y)$) takes less than 15 minutes 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. TI - An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications KW - algorithms KW - computation KW - mathematics KW - printed KW - quantum AU - Casas, Fernando AU - Murua, Ander PY - 2008/Oct/15/ UR - http://arxiv.org/abs/0810.2656 ER -