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

DOI:
https://doi.org/10.1090/S0025-5718-03-01540-0

Published electronically:
July 14, 2003

MathSciNet review:
2034119

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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate the integral

where or or and 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.

**1.**G. Criscuolo, A new algorithm for Cauchy principal value and Hadamard finite-part integrals, J. Comp. and Appl. Math. 78, 1997, pp.255-275. MR**98b:65025****2.**G. Criscuolo, G. Mastroianni, Mean and uniform convergence of quadrature rules for evaluating the finite Hilbert transform, in: Progress In Approximation Theory (P. Nevai, A. Pinkus, eds.), Academic Press, Boston, 1991, pp.141-175. MR**92f:65035****3.**G. Criscuolo, G. Mastroianni, P. Nevai, Associated generalized Jacobi functions and polynomials, J. Math. Anal. and Appl. 158, 1991, pp.15-34. MR**92h:33018****4.**Z. Ditzian, V. Totik, Moduli of Smoothness, Springer Verlag, Heidelberg, 1987. MR**89h:41002****5.**G. Mastroianni, M.R. Russo, Lagrange interpolation in some weighted uniform spaces, Facta Universitatis, ser. Math. Inform. 12, 1997, pp.185-201. MR**99m:41004****6.**G. Mastroianni, G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 70, 2001, pp.251-267. MR**2002e:65208****7.**P. Nevai, Orthogonal Polynomials, Mem. Amer. Math. Soc. 18, n. 213, 1979. MR**80k:42025****8.**G. Szegö, Orthogonal Polynomials, Amer. Math. Soc., vol. 23, Providence, R.I., 1975. MR**51:8724**

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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

Email:
criscuo@matna2.dma.unina.it

DOI:
https://doi.org/10.1090/S0025-5718-03-01540-0

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