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On the convergence and optimization of the Baker–Campbell–Hausdorff formula

✍ Scribed by Sergio Blanes; Fernando Casas

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
296 KB
Volume
378
Category
Article
ISSN
0024-3795

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✦ Synopsis

In this paper the problem of the convergence of the Baker-Campbell-Hausdorff series for Z = log(e X e Y ) is revisited. We collect some previous results about the convergence domain and present a new estimate which improves all of them. We also provide a new expression of the truncated Lie presentation of the series up to sixth degree in X and Y requiring the minimum number of commutators. Numerical experiments suggest that a similar accuracy is reached with this approximation at a considerably reduced computational cost.

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