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Cheney, E. W.; Rivlin, T. J.

Some polynomial approximation operators. (English) Zbl 0295.41003

Math. Z. 145, 33-42 (1975).
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Cited in 1 Review
Cited in 8 Documents

MSC:

41A10 Approximation by polynomials
41A35 Approximation by operators (in particular, by integral operators)
41A50 Best approximation, Chebyshev systems
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Full Text: DOI EuDML

References:

[1] Bernstein, S.: Sur la limitation des valeurs d’un polynomeP n(x) de degrén sur tout un segment par ses valeurs enn+1 points du segment. Izvestija Akad. Nauk SSSR, Otd?l. mat. i estest. Nauk, VII Ser., Nr. 8, 1025?1050 (1931)
[2] Ehlich, H., Zeller, K.: Auswertung der Normen von Interpolations-Operatoren. Math. Ann.164, 105?112 (1966) · Zbl 0136.04604 · doi:10.1007/BF01429047
[3] Erdös, P.: Problems and results in the theory of interpolation, II. Acta. math. Acad. Sci. Hungar.12, 235?244 (1961) · Zbl 0098.04103 · doi:10.1007/BF02066686
[4] Kilgore, T.A., Cheney, E.W.: A theorem on interpolation in Haar subspaces. To appear, Aequationes math. · Zbl 0327.41001
[5] La Vallée Poussin, C. de: Sur la méthode de l’approximation minimum. Ann. Soc. sci. Bruxelles, 2e Partie,35, 1?16 (1911) · JFM 42.0255.02
[6] Luttmann, F.W., Rivlin, T.J.: Some numerical experiments in the theory of polynomial interpolation. IBM J. Res. Develop.9, 187?191 (1965) · doi:10.1147/rd.93.0187
[7] McCabe, J.H., Phillips, G.M.: On a certain class of Lebesgue Constants. BIT, Nordisk Tidskr. Inform.-behandl.13, 434?442 (1973) · Zbl 0274.41002
[8] Morris, P.D., Cheney, E.W.: On the existence and characterization of minimal projections. J. reine angew. Math.270, 61?76 (1974) · Zbl 0303.41037
[9] Morris, P.D., Price, K.H., Cheney, E.W.: On a approximation operator of de La Vallée Poussin. J. Approximation Theory13, 375?391 (1975) · Zbl 0312.41010 · doi:10.1016/0021-9045(75)90021-0
[10] Motzkin, T.S., Sharma, A.: Next-to-interpolatory approximation on sets with multiplicities. Canadian J. Math.18, 1196?1211 (1966) · Zbl 0152.25402 · doi:10.4153/CJM-1966-118-7
[11] Motzkin, T.S., Sharma, A.: A sequence of linear polynomial operators and their approximation theoretic properties. J. Approximation Theory5, 176?198 (1972) · Zbl 0237.41002 · doi:10.1016/0021-9045(72)90038-X
[12] Pólya, G., Szegö, G.: Aufgaben und Lehrsätze aus der Analysis II. Berlin: Springer 1924 · Zbl 0060.12307
[13] Powell, M.J.D.: On the maximum errors of polynomial approximation defined by interpolation and by least squares criteria. Computer J.9, 404?407 (1967) · Zbl 0147.14305 · doi:10.1093/comjnl/9.4.404
[14] Riesz, M.: Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome. J.-ber. Deutsch. Math.-Verein.23, 354?368 (1914) · JFM 45.0405.02
[15] Rivlin, T.J.: An Introduction to the Approximation of Functions. Waltham-Toronto-London: Blaisdell 1969 · Zbl 0189.06601
[16] Rivlin, T.J.: The Chebyshev Polynomials. New York: Wiley-Interscience 1974 · Zbl 0299.41015
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