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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 \[ \int _a^b \int _{-1}^1\frac {f(x,y)}{x-y}dxdy, \] 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