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

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-06-02 DOI:10.1016/j.amc.2025.129563

Ana Arnal, Fernando Casas, Cristina Chiralt

引用次数: 0

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.

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一个计算连续Baker-Campbell-Hausdorff公式的有效程序

给出了一种基于Magnus展开的连续Baker-Campbell-Hausdorff公式的有效计算方法。它只需要计算一个迭代积分和一个新的对易子在每一次。剩下的项通过置换对迭代积分指标的作用得到恢复。通过几个控制理论的例子说明了这个过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.