一种基于素数分解的索引拆分计算Bell多项式快速算法
A fast algorithm for computing Bell polynomials based on index break-downs using prime factorization
AI总结：
提出一种基于素数分解的索引拆分快速算法，利用Bell多项式与有理卷积幂的联系，显著减少计算部分Bell多项式的算术运算量。
摘要：
通过建立普通Bell多项式与有理卷积幂之间的有趣联系，获得了Bell多项式的一些复合与逆关系，以及序列卷积根的显式表达式。基于这些结果，提出了一种基于素数分解计算部分Bell多项式的新方法。结果表明，在大多数情况下，该方法比传统的递推过程计算Bell多项式更高效，所需算术运算量远少。提供了计算复杂度的详细分析，并进行了数值评估。
英文摘要：
By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are obtained. Based on these results, a new method is proposed for calculation of partial Bell polynomials based on prime factorization. It is shown that this method is more efficient than the conventional recurrence procedure for computing Bell polynomials in most cases, requiring far less arithmetic operations. A detailed analysis of the computation complexity is provided, followed by some numerical evaluations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
