AI 中文总结
本文提出一种更简单的稳定数值多项式乘法算法，保持相同时间复杂度和误差界，并可加速近凸min-plus卷积问题求解。
AI 中文摘要
在预印本[vdH08]中，van der Hoeven考虑了将两个具有浮点系数的多项式相乘的问题，并给出了一种算法，该算法在时间$O(np \log(np))$内计算具有较小相对牛顿误差的乘积，其中$n$是次数，$p$是所需精度。在本文中，我们描述了一种显著更简单的算法，具有相同的时间复杂度和误差界。独立地，Bringmann和Cassis在[BC23a]中考虑了近凸min-plus卷积问题，并提出了一种解决该问题的算法。我们观察到，我们的算法可以适用于该问题，从而将Bringmann和Cassis的算法加速一个对数因子。
英文摘要
In the preprint [vdH08], van der Hoeven considers the problem of multiplying two polynomials with floating-point coefficients, and give an algorithm to compute the product with small relative Newton error in time $O(np \log(np))$, where $n$ is the degree and $p$ is the required precision. In this paper, we describe a significantly simpler algorithm with the same time complexity and error bound. Independently, Bringmann and Cassis considered the near-convex min-plus convolution problem in [BC23a], and presented an algorithm to solve that problem. We observe that our algorithm can be adapted to that problem to speed up Bringmann and Cassis' algorithm by a logarithmic factor.
Comments29 pages, 7 figures
