Essentially Optimal Sparse Polynomial Multiplication
Symbolic Computation
2020-09-01 v2 Computational Complexity
Data Structures and Algorithms
Abstract
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.
Cite
@article{arxiv.2001.11959,
title = {Essentially Optimal Sparse Polynomial Multiplication},
author = {Pascal Giorgi and Bruno Grenet and Armelle Perret du Cray},
journal= {arXiv preprint arXiv:2001.11959},
year = {2020}
}
Comments
12 pages