Chunky和n-空间多项式乘法
Chunky and Equal-Spaced Polynomial Multiplication
摘要：
求两个多项式的乘积是计算机代数中的一个基本问题。虽然大多数以前的结果都集中在最坏情况下的复杂性，而不是采用自适应分析的技术，在许多“简单”的情况下，给一个改进。我们提出了两个自适应措施和方法的多项式乘法，并展示了如何有效地结合起来，以获得这两个优点。这些算法的一个有用的特征是，它们本质上提供了现有的“稀疏”和“密集”方法之间的梯度。我们证明，这些方法提供了显着的改善，在许多情况下，但在最坏的情况下，仍然是最快的现有算法相媲美。
英文摘要：
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement in many "easy" cases. We present two adaptive measures and methods for polynomial multiplication, and also show how to effectively combine them to gain both advantages. One useful feature of these algorithms is that they essentially provide a gradient between existing "sparse" and "dense" methods. We prove that these approaches provide significant improvements in many cases but in the worst case are still comparable to the fastest existing algorithms.
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