多项式运算的快速原地算法：除法、求值、插值
Fast In-place Algorithms for Polynomial Operations: Division, Evaluation, Interpolation
摘要：
我们考虑节省空间的版本上的几个重要的操作单变量多项式，即幂级数反演和除法，除法与剩余，多点评估，插值。现在经典的结果表明，这样的问题可以解决（几乎）相同的渐近时间快速多项式乘法。然而，这些减少，即使当应用于快速多项式乘法的原地变体时，也会产生需要至少线性量的额外空间用于中间结果的算法。我们展示了新的在上述多项式计算，只需要恒定的额外空间，并实现相同的渐近运行时间，因为他们的位置对应的算法。我们还提供了一个精确的复杂性分析，使所有常数显式，参数化的基础乘法算法的空间使用。
英文摘要：
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that such problems can be solved in (nearly) the same asymptotic time as fast polynomial multiplication. However, these reductions, even when applied to an in-place variant of fast polynomial multiplication, yield algorithms which require at least a linear amount of extra space for intermediate results. We demonstrate new in-place algorithms for the aforementioned polynomial computations which require only constant extra space and achieve the same asymptotic running time as their out-of-place counterparts. We also provide a precise complexity analysis so that all constants are made explicit, parameterized by the space usage of the underlying multiplication algorithms.
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。
