# On Fast Computation of a Circulant Matrix-Vector Product

arXiv: https://arxiv.org/abs/2103.02605 · HTML: https://mlsanity.com/paper/2103.02605/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [FastRPB: a Scalable Relative Positional Encoding for Long Sequence Tasks](https://mlsanity.com/paper/2202.11364/) (2022)

## Abstract (arXiv)

This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of a factor of about 2.25 for the multiplication of two polynomials with integer coefficients compared to multiplication by an FFT algorithm. Moreover this paper discusses multiplication of large integers as further application.