# A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

Xu, Kuan, Austin, Anthony P., Wei, Ke (2017) A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions. SIAM Journal on Scientific Computing, 39 (6). A3089-A3106. ISSN 1064-8275. E-ISSN 1095-7197. (doi:10.1137/17M1114764) (KAR id:58502)

 PDF Publisher pdf Language: English Download (48kB) This file may not be suitable for users of assistive technology. Request an accessible format Official URLhttps://doi.org/10.1137/17M1114764

## Abstract

We present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. The complexity of the algorithm is $\mathcal{O}\bigl(N (\log N)^2\bigr)$, where $N$ is the number of degrees of freedom used in each of the Fourier extensions.

Item Type: Article 10.1137/17M1114764 Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Kuan Xu 09 Nov 2016 18:13 UTC 16 Feb 2021 13:39 UTC https://kar.kent.ac.uk/id/eprint/58502 (The current URI for this page, for reference purposes)