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Bounds for the number of nodes in Chebyshev type quadrature formulas. (English) Zbl 0751.41026

The authors determine an upper bound for the minimum number of nodes of Chebyshev type quadrature formulas on a finite interval needed in order to achieve a certain degree of precision, using a topological method. The corresponding problem on the \(d\)-dimensional sphere is studied also.
Reviewer: P.Narain (Bombay)

MSC:

41A55 Approximate quadratures
Full Text: DOI

References:

[1] de Reyna, J. Arias, A generalized mean-value theorem, Monatsh. Math., 106, 95-97 (1988) · Zbl 0689.26002
[3] (Collected Works, Vol. II (1954), Izdat. Akad. Nauk SSSR: Izdat. Akad. Nauk SSSR Moscow), 200-204, (Russian) · Zbl 0016.15902
[4] Boas, R. P., Inequalities for the derivatives of polynomials, Math. Mag., 42, 165-174 (1969) · Zbl 0179.37803
[5] Costabile, F., Sulle formule di quadratura di Tschebyscheff, Calcolo, 11, 191-200 (1974) · Zbl 0296.65009
[6] Delsarte, P.; Goethals, J. M.; Seidel, J. J., Spherical codes and designs, Geom. Dedicata, 6, 363-388 (1977) · Zbl 0376.05015
[7] Gautschi, W., Advances in Chebyshev quadrature, (Watson, G. A., Numerical Analysis. Numerical Analysis, Lecture Notes in Math., Vol. 506 (1976), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0331.65016
[8] Meier, A.; Sharma, A., A variation on the Tchebicheff quadrature problem, Illinois J. Math., 11, 535-546 (1967) · Zbl 0175.06302
[9] Seymour, P.; Zaslavsky, T., Averaging sets: A generalization of mean values and spherical designs, Adv. in Math., 52, 213-240 (1984) · Zbl 0596.05012
[10] Sierpinski, W., (Schinzel, A., Elementary Theory of Numbers (1987), Polish Sci. Publ: Polish Sci. Publ Warszawa) · Zbl 0638.10001
[11] Stroud, A. H., Approximate Calculation of Multiple Integrals (1971), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0379.65013
[12] Szegő, G., Orthogonal Polynomials, (Amer. Math. Soc. Colloquium Publ., Vol. 23 (1939)) · JFM 65.0278.03
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