论文标题
本质上是最佳的稀疏多项式乘法
Essentially Optimal Sparse Polynomial Multiplication
论文作者
论文摘要
我们提出了一种概率算法，以在一个字段上计算两个单变量稀疏多项式的乘积，其中许多位操作在输入和输出的大小和输出的大小中是Quasi线性的。我们的算法适用于任何特征性零或大于程度的领域。我们主要依靠稀疏的插值和新算法来验证具有准线性时间复杂性的稀疏产品。使用Kronecker替代技术，我们将结果扩展到多元案例。
We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output. Our algorithm works for any field of characteristic zero or larger than the degree. We mainly rely on sparse interpolation and on a new algorithm for verifying a sparse product that has also a quasi-linear time complexity. Using Kronecker substitution techniques we extend our result to the multivariate case.
