Faster polynomial multiplication via multipoint Kronecker substitution

TL;DR

This paper introduces new algorithms for dense polynomial multiplication using multipoint Kronecker substitution, significantly enhancing performance for moderately sized inputs both theoretically and empirically.

Contribution

The paper presents novel algorithms that improve upon standard Kronecker substitution for polynomial multiplication, offering better efficiency for certain input sizes.

Findings

Improved theoretical complexity bounds for the new algorithms.

Empirical tests show performance gains over standard methods.

Algorithms are particularly effective for moderately sized polynomials.

Abstract

We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a sizeable constant, both in theory and in empirical tests.