A generalized FFT for Clifford algebras

Paul Leopardi

doi:10.36045/bbms/1110205626

A generalized FFT for Clifford algebras

Paul Leopardi

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	663-688
Number of pages	26
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	11
Issue number	5
DOIs	https://doi.org/10.36045/bbms/1110205626
Publication status	Published - Dec 2004
Externally published	Yes

Access to Document

10.36045/bbms/1110205626

Cite this

@article{d3dc67170ad548ffad6ac0c7800f0419,

title = "A generalized FFT for Clifford algebras",

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.",

keywords = "Clifford algebras, Generalized FFT, Linear complexity, Real matrix representations",

author = "Paul Leopardi",

year = "2004",

month = dec,

doi = "10.36045/bbms/1110205626",

language = "English",

volume = "11",

pages = "663--688",

journal = "Bulletin of the Belgian Mathematical Society - Simon Stevin",

issn = "1370-1444",

publisher = "Belgian Mathematical Society",

number = "5",

}

TY - JOUR

T1 - A generalized FFT for Clifford algebras

AU - Leopardi, Paul

PY - 2004/12

Y1 - 2004/12

N2 - 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.

AB - 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.

KW - Clifford algebras

KW - Generalized FFT

KW - Linear complexity

KW - Real matrix representations

UR - http://www.scopus.com/inward/record.url?scp=17044393633&partnerID=8YFLogxK

U2 - 10.36045/bbms/1110205626

DO - 10.36045/bbms/1110205626

M3 - Article

SN - 1370-1444

VL - 11

SP - 663

EP - 688

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 5

ER -

A generalized FFT for Clifford algebras

Abstract

Access to Document

Other files and links

Fingerprint

Cite this