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On the existence of optimal integration formulas for analytic functions. (English) Zbl 0279.65019


MSC:

65D30 Numerical integration
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
41A55 Approximate quadratures
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References:

[1] Davis, P.: Interpolation and approximation. New York: Blaisdell 1963 · Zbl 0111.06003
[2] Richter-Dyn, N.: Properties of minimal integration rules II. SIAM J. Numer. Anal.8, 497-508 (1971) · Zbl 0229.65017 · doi:10.1137/0708047
[3] Barrar, R. B., Loeb, H. L.: Analytic extended monosplines. Num. Math.22, 119-125 (1974) · Zbl 0265.65012 · doi:10.1007/BF01436726
[4] Karlin, S., Studden, W. S.: Tchebycheff systems: With applications in analysis and statistics. Pure and Appl. Math. Vol. 15. New York: Interscience 1966 · Zbl 0153.38902
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[7] Richter-Dyn, N.: Properties of minimal integration rules. SIAM J. Numer. Anal.7, 61-79 (1970) · Zbl 0222.65023
[8] Richter-Dyn, N.: Minimal interpolation and approximation in Hilbert spaces. SIAM J. Num. Anal.8, 583-597 (1971) · Zbl 0229.65016 · doi:10.1137/0708056
[9] Eckhardt, U.: Einige Eigenschaften Wilfscher Quadraturen. Num. Math.2, 1-7 (1968) · Zbl 0165.51002 · doi:10.1007/BF02170990
[10] Karlin, S.: On a class of non-linear approximation problems. Bulletin Amer. Math. Soc.18, 43-48 (1972) · Zbl 0229.41009 · doi:10.1090/S0002-9904-1972-12842-8
[11] Bergman, S.: The Kernel functions and conformal mapping. Mathematical Surveys, No. 5, American Math. Soc., 1950 · Zbl 0040.19001
[12] Meschkowski, H.: Hilbertsche Räume mit Kernfunktion. Berlin-Göttingen-Heidelberg: Springer 1962 · Zbl 0103.08802
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