Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Pointwise simultaneous convergence of extended Lagrange interpolation with additional knots

Authors: Giuliana Criscuolo, Giuseppe Mastroianni and Péter Vértesi
Journal: Math. Comp. 59 (1992), 515-531
MSC: Primary 41A05; Secondary 65D05
MathSciNet review: 1134723
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] V. M. Badkov, Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval, Math. USSR-Sb. 24 (1974), 223-256. MR 0355464 (50:7938)
  • [2] G. Criscuolo, G. Mastroianni, and D. Occorsio, Convergence of extended Lagrange interpolation, Math. Comp. 55 (1990), 197-212. MR 1023044 (91c:65008)
  • [3] G. Criscuolo and G. Mastroianni, Mean and uniform convergence of quadrature rules for evaluating the finite Hilbert transform, Progress in Approximation Theory (P. Nevai and A. Pinkus, eds.), Academic Press, 1991, pp. 141-176. MR 1114771 (92f:65035)
  • [4] V. K. Dzjadik, Introduction to uniform approximation of functions by polynomials, Nauka, Moscow, 1977. (Russian) MR 0612836 (58:29579)
  • [5] W. Gautschi, Gauss-Kronrod quadrature--A survey, Numerical Methods and Approximation Theory III (G. V. Milovanović, ed.), Prosveta, Niš, 1988, pp. 39-66. 6. G. Monegato, Stieltjes polynomials and related quadrature rules, SIAM Rev. 24 (1982), 137-158. MR 960329 (89k:41035)
  • [7] P. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc., No. 213 (1979). MR 519926 (80k:42025)
  • [8] P. Nevai and P. Vértesi, Mean convergence of Hermite-Fejér interpolation, J. Math. Anal. Appl. 105 (1985), 26-58. MR 773571 (86h:41004)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 41A05, 65D05

Retrieve articles in all journals with MSC: 41A05, 65D05

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society