Authors: Stanković, Radomir 
Astola, Jaakko
Moraga, Claudio
Stanković, Stanislav
Title: Remarks on efficient computation of the inverse Fourier transforms on finite non-Abelian groups
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 6928 LNCS
Issue: PART 2
First page: 288
Last page: 295
Conference: 13th International Conference on Computer Aided Systems Theory, EUROCAST 2011; Las Palmas de Gran Canaria; Spain; 6 February 2011 through 11 February 2011
Issue Date: 20-Feb-2012
Rank: M33
ISBN: 978-3-642-27578-4
ISSN: 0302-9743
DOI: 10.1007/978-3-642-27579-1_37
The Fourier transform is a classical method in mathematical modeling of systems. Assuming finite non-Abelian groups as the underlying mathematical structure might bring advantages in modeling certain systems often met in computer science and information technologies. Frequent computing of the inverse Fourier transform is usually required in dealing with such systems. These computations require for each function value to compute many times traces of certain matrices. These matrices are products of matrix-valued entries of unitary irreducible representations and matrix-valued Fourier coefficients. In the case of large non-Abelian groups the complexity of these computations can be a limiting factor in applications. In this paper, we present a method for speeding-up computing the traces by using decision diagrams to operate on matrix-valued group representations and related Fourier coefficients.
Keywords: decision diagrams | Fourier transform | non-Abelian groups | Systems on groups
Publisher: Springer Link

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