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March 2005 A generalized FFT for Clifford algebras
Paul Leopardi
Bull. Belg. Math. Soc. Simon Stevin 11(5): 663-688 (March 2005). DOI: 10.36045/bbms/1110205626

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.

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Paul Leopardi. "A generalized FFT for Clifford algebras." Bull. Belg. Math. Soc. Simon Stevin 11 (5) 663 - 688, March 2005. https://doi.org/10.36045/bbms/1110205626

Information

Published: March 2005
First available in Project Euclid: 7 March 2005

zbMATH: 1071.65190
MathSciNet: MR2130632
Digital Object Identifier: 10.36045/bbms/1110205626

Keywords: Clifford algebras , Generalized FFT , linear complexity , real matrix representations

Rights: Copyright © 2005 The Belgian Mathematical Society

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Vol.11 • No. 5 • March 2005
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