Numerical approximation of weakly singular integrals on the half line
type: Item
instance of: scholarly article
title: Numerical approximation of weakly singular integrals on the half line
zbMATH Open document ID: 1029.65025
DOI: 10.1016/S0377-0427(01)00411-3
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The authors construct a quadrature approximation \(K_m\) to operators of the type \[ K(f,t)=\int_0^\infty {f(x)\over |x-t|^\lambda} \sqrt{w_\alpha(x)} dx, \] where \(w_\alpha\) is the Laguerre weight, \(t\geq 0\) and \(0<\lambda<1\), such that \[ \sup_{t\geq 0} |K(f,t)-K_m(f,t)|\leq {\mathcal C} [E_M(f)_u +e^{-Am}\|fu\|] \log m, \] whre \( E_M(f)_u \) is the error of best approximation in the weighted uniform norm, \(M\sim m\) and the positive constants \({\mathcal C}\) and \(A\) are independent of \(m,f\). The method is based on the Laguerre nodes and on ``truncating'' \(f\) for \(x>4\theta m\), \(0<\theta<1\). The numerical stability is shown, and a method for computing the weights and several numerical examples are given.
reviewed by: Sven Ehrich
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 1758448
zbMATH Keywords: weakly singular integrals
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: error bound
zbMATH Keywords: quadrature
zbMATH Keywords: numerical stability
zbMATH Keywords: numerical examples
author: Giuseppe Mastroianni
author: Donatella Occorsio
MaRDI profile type: Publication
cites work: Approximation of the Hilbert transform on the real semiaxis using Laguerre zeros
cites work: Jackson and smoothness theorems for Freud weights in \(L_ p (0<p\leq\infty)\)
cites work: Nystroem interpolants based on zeros of Laguerre polynomials for some Weiner-Hopf equations
cites work: Lagrange interpolation at Laguerre zeros in some weighted uniform spaces
cites work: Q3693982
cites work: Numerical analysis for integral and related operator equations.
cites work: Where are the nodes of ''good'' interpolation polynomials on the real line?
cites work: Q4061445
description: scientific article; zbMATH DE number 1758448