## Bulletin of the Belgian Mathematical Society - Simon Stevin

### A generalized FFT for Clifford algebras

Paul Leopardi

#### Abstract

This paper describes a relationship between fast real matrix representations of real universal Clifford algebras and the generalized Fast Fourier Transform for supersolvable groups. Detailed constructions of algorithms for the forward and inverse representations for Clifford algebras are given, with proof that these need at most $O(d \log d)$ operations. The algorithms have been implemented and tested in the GluCat C++ library, and some timing results are included.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 5 (2005), 663-688.

Dates
First available in Project Euclid: 7 March 2005

https://projecteuclid.org/euclid.bbms/1110205626

Digital Object Identifier
doi:10.36045/bbms/1110205626

Mathematical Reviews number (MathSciNet)
MR2130632

Zentralblatt MATH identifier
1071.65190

#### Citation

Leopardi, Paul. A generalized FFT for Clifford algebras. Bull. Belg. Math. Soc. Simon Stevin 11 (2005), no. 5, 663--688. doi:10.36045/bbms/1110205626. https://projecteuclid.org/euclid.bbms/1110205626