Sparse discretization matrices for Volterra integral operators with applications to numerical differentiation
type: Item
instance of: scholarly article
title: Sparse discretization matrices for Volterra integral operators with applications to numerical differentiation
zbMATH Open document ID: 1246.65255
DOI: 10.1216/JIE-2011-23-1-137
author: Haizhang Zhang
author: Qinghui Zhang
published in: Journal of Integral Equations and Applications
publication date: 2011-06-30T00:00:00Z
review text: The authors study the numerical solution of Volterra integral equations of the first kind. It is supposed a finite dimensional feature space or, equivalently, that the integral kernel has finite rank. This allows the construction of orthonormal bases with small support that is preserved by the integral operator. In particular, the proposed method is based on the Tikhonov regularization and the projection method with respect to the constructed orthonormal basis that provides a sparse discretization of the Tikhonov operator. An example of a basis functions with the required properties are obtained by using wavelet bases. The paper concludes with the application of the proposed method to the solution of the integral equation arising from the numerical differentiation problem.
reviewed by: P. Maponi
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 5915501
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: numerical differentiation
zbMATH Keywords: wavelet basis
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: projection methods
zbMATH Keywords: lossless compression
zbMATH Keywords: refinable vector field
describes a project that uses: GCVSPL
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5915501