Q2001762
type: Item
instance of: scholarly article
title: Wavelet approximation of functions belonging to generalized Lipschitz class by extended Haar wavelet series and its application in the solution of Bessel differential equation using Haar operational matrix
zbMATH Open document ID: 1422.42047
author: Shyam Lal
author: Priya Kumari
published in: International Journal of Applied and Computational Mathematics
publication date: 2019-07-11T00:00:00Z
review text: The authors define a generalized Haar wavelet, whose basis functions are supported on intervals of length \(1/\mu\), \(\mu \ge 1\) integer, instead of \([0,1]\). They also consider a generalization of Lipschitz continuity, where functions in the class Lip\(_\alpha^{(s)}[0,1)\) satisfy \[ |f(x) - f(x+t)| \le C s(t) |t|^\alpha, \quad x, x+t \in [0,1), \] with \(s(t) |t|^\alpha \to 0\) as \(t \to 0\). They generalize existing results on best approximation for Lipschitz continuous functions by Haar wavelets, and apply this to estimate the accuracy of the numerical solution of the differential equation for the 0th order Bessel function by wavelet methods.
reviewed by: Fritz Keinert
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 7078985
zbMATH Keywords: Lipschitz class
zbMATH Keywords: generalized Haar wavelet
zbMATH Keywords: best approximation
MaRDI profile type: Publication
full work available at URL: s40819-019-0646-7
OpenAlex ID: W2944272574
Wikidata QID: Q115372396
cites work: Q4003151
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cites work: Wavelet packet approximation
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cites work: Q2760584
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DOI: 10.1007/S40819-019-0646-7
label: Wavelet approximation of functions belonging to generalized Lipschitz class by extended Haar wavelet series and its application in the solution of Bessel differential equation using Haar operational matrix
description: scientific article; zbMATH DE number 7078985