论文标题
一种基于索引分解的快速算法，用于计算钟形多项式，使用质量分解
A fast algorithm for computing Bell polynomials based on index break-downs using prime factorization
论文作者
论文摘要
通过建立普通的钟形多项式与理性卷积能力之间的有趣联系，获得了贝尔多项式的某些组成和反比关系以及序列卷积根的显式表达。基于这些结果，提出了一种新方法，用于根据主要分解计算部分钟形多项式。结果表明，该方法比在大多数情况下计算钟形多项式的常规复发程序更有效，需要降低算术操作。提供了对计算复杂性的详细分析，然后进行一些数值评估。
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.
