An efficient procedure to compute the continuous Baker–Campbell–Hausdorff formula

Ana Arnal, Fernando Casas and Cristina Chiralt

Applied Mathematics and Computation, 2025, vol. 507, issue C

Abstract: We present an efficient procedure to compute the continuous Baker–Campbell–Hausdorff formula based on the Magnus expansion. It only requires the computation of one iterated integral and one new commutator at each degree. The remaining terms are recovered by the action of permutations on the indices of the iterated integral. The procedure is illustrated on several examples of control theory.

Keywords: Continuous BCH formula; Logarithm of the Chen–Fliess series; Magnus expansion; Control theory (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325002899

DOI: 10.1016/j.amc.2025.129563

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