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


References [Enhancements On Off] (What's this?)

  • 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$^{\rm o}$. 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

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