Pointwise simultaneous convergence of extended Lagrange interpolation with additional knots
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- by Giuliana Criscuolo, Giuseppe Mastroianni and Péter Vértesi PDF
- Math. Comp. 59 (1992), 515-531 Request permission
Abstract:
In numerical analysis it is important to construct interpolating polynomials approximating a given function and its derivatives simultaneously. The authors define some new good interpolating matrices with "many" nodes close to the endpoints of the interval and also give error estimates.References
- V. M. Badkov, Convergence in the mean and almost everywhere of Fourier series in polynomials that are orthogonal on an interval, Mat. Sb. (N.S.) 95(137) (1974), 229–262, 327 (Russian). MR 0355464
- Giuliana Criscuolo, Giuseppe Mastroianni, and Donatella Occorsio, Convergence of extended Lagrange interpolation, Math. Comp. 55 (1990), no. 191, 197–212. MR 1023044, DOI 10.1090/S0025-5718-1990-1023044-X
- Giuliana Criscuolo and Giuseppe Mastroianni, Mean and uniform convergence of quadrature rules for evaluating the finite Hilbert transform, Progress in approximation theory, Academic Press, Boston, MA, 1991, pp. 141–175. MR 1114771
- V. K. Dzyadyk, Vvedenie v teoriyu ravnomernogo priblizheniya funktsiĭ polinomami, Izdat. “Nauka”, Moscow, 1977 (Russian). MR 0612836
- Walter Gautschi, Gauss-Kronrod quadrature—a survey, Numerical methods and approximation theory, III (Niš, 1987) Univ. Niš, Niš, 1988, pp. 39–66. MR 960329
- Paul G. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 18 (1979), no. 213, v+185. MR 519926, DOI 10.1090/memo/0213
- Paul Nevai and Péter Vértesi, Mean convergence of Hermite-Fejér interpolation, J. Math. Anal. Appl. 105 (1985), no. 1, 26–58. MR 773571, DOI 10.1016/0022-247X(85)90095-2
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Math. Comp. 59 (1992), 515-531
- MSC: Primary 41A05; Secondary 65D05
- DOI: https://doi.org/10.1090/S0025-5718-1992-1134723-X
- MathSciNet review: 1134723