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A note on a paper by G. Mastroianni and G. Monegato

Author: G. Criscuolo
Journal: Math. Comp. 73 (2004), 243-250
MSC (2000): Primary 41A55; Secondary 65D32, 65N38
Published electronically: July 14, 2003
MathSciNet review: 2034119
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Abstract: Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate the integral

\begin{displaymath}\int_a^b \int_{-1}^1\frac{f(x,y)}{x-y}dxdy, \end{displaymath}

where $(a,b)\equiv (-1,1)$ or $(a,b)\equiv(a,-1)$ or $(a,b)\equiv (1,b)$ and $f(x,y)$ is a smooth function (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 70 2001, 251-267). The error bounds for the quadrature rule approximating the inner integral given in Theorems 3, 4 of that paper are not correct according to the proof. However, following a different approach, we are able to improve the pointwise error estimates given in that paper.

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Additional Information

G. Criscuolo
Affiliation: Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Napoli “Federico II”, Complesso Monte Sant’Angelo, Edificio T, Via Cintia, 80126 Napoli, Italy

Keywords: Singular integrals, error estimates, Lagrange operator, functions of the second kind
Received by editor(s): March 22, 2002
Published electronically: July 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society