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A note on a paper by G. Mastroianni and G. Monegato
Author(s):
G.
Criscuolo.
Journal:
Math. Comp.
73
(2004),
243-250.
MSC (2000):
Primary 41A55;
Secondary 65D32, 65N38
Posted:
July 14, 2003
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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.
References:
- 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:
10.1090/S0025-5718-03-01540-0
PII:
S 0025-5718(03)01540-0
Keywords:
Singular integrals,
error estimates,
Lagrange operator,
functions of the second kind
Received by editor(s):
March 22, 2002
Posted:
July 14, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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