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On the uniform convergence of interpolatory polynomials

Part of: Approximations and expansions

Published online by Cambridge University Press:  09 April 2009

J. Prasad
J. Prasad
Affiliation:
Department of MathematicsCalifornia State UniversityLos Angeles, California 90032, U.S.A.
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Abstract

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Here we consider a problem on weighted (0, 2) interpolation. We choose the interpolatory conditions in such a way that we get the polynomial of degree ≤2n−1, satisfying those conditions. Moreover we prove that the sequence of these interpolatory polynomials under certain conditions converges uniformly to a function belonging to the Zygmund class.

MSC classification

Secondary: 41A25: Rate of convergence, degree of approximation
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 7 - 16
Copyright
Copyright © Australian Mathematical Society 1979

References

Balázs, J. (1961), ‘Súlyozott (0, 2) interpolácio Ultrazférikus polinomok gyökein’, Magyar Tud. Akad. Math. Fiz. Ozst. Közl. 11 (3), 305–338.Google Scholar
Balázs, J. and Turán, P. (1958), ‘Notes on interpolation II’, Acta Math. Acad. Sci. Hungar. 8, 201–215.CrossRefGoogle Scholar
Freud, G. (1958), ‘Bemerkung über die Konvergenz eines Interpolations-Verfahrens von P. Turán’, Acta Math. Acad. Sci. Hungar. 9, 337–341.CrossRefGoogle Scholar
Prasad, J. (1970), ‘On the weighted (0, 2) interpolation’, SIAM J. Numer. Anal. 7 (3), 428–446.CrossRefGoogle Scholar
Prasad, J. (1972–1973), ‘(0, 2) interpolation on Legendre abscissas’, Math. Notae 23, 25–34.Google Scholar
Prasad, J. and Eckert, E. J. (1973), ‘On the representation of functions by interpolatory polynomials’, Mathematica (Cluj) 15 (38), 2, 289–305.Google Scholar
Prasad, J. and Varma, A. K. (1969), ‘An analogue of a problem of J. Balázs and P. Turán’, Canad. J. Math. 21, 54–63.CrossRefGoogle Scholar
Sansone, G. (1959), Orthogonal functions (Interscience, New York).Google Scholar
Surányi, J. and Turán, P. (1955), ‘Notes on interpolation I’, Acta Math. Acad. Sci. Hungar. 6, 67–79.CrossRefGoogle Scholar
Szegö, G. (1959), Orthogonal polynomials (Amer. Math. Soc. Colloq. Publ. vol. 23).Google Scholar