Harmonic analysis for graph refinements and the continuous graph FFT
type: Item
instance of: scholarly article
title: Harmonic analysis for graph refinements and the continuous graph FFT
zbMATH Open document ID: 1167.65077
author: J. Martínez
published in: Linear Algebra and its Applications
publication date: 2009-06-04T00:00:00Z
review text: The discrete Fourier transforms (DFT) and their fast algorithms (FFT) are extended to continuous graphs with equal edge lengths. After a review of differential operators on continuous graphs, the spectral theory of standard Laplace differential operators for continuous graphs and their uniformly sampled subgraphs is explored. After these preliminaries, a continuous graph DFT is defined. Fast algorithms for this DFT and its inverse are described. Finally, an example is presented.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 34B45
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 05C85
Mathematics Subject Classification ID: 94C15
zbMATH DE Number: 5561694
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: fast Fourier transform (FFT)
zbMATH Keywords: continuous graph FFT
zbMATH Keywords: graph spectral theory
zbMATH Keywords: graph refinements
zbMATH Keywords: harmonic analysis
zbMATH Keywords: numerical example
zbMATH Keywords: Laplace differential operators
MaRDI profile type: Publication
full work available at URL: j.laa.2008.12.035
OpenAlex ID: W2040633625
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DOI: 10.1016/J.LAA.2008.12.035
description: scientific article; zbMATH DE number 5561694