On a conjecture of D. B. Hunter |
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Authors: | Helmut Brass Knut Petras |
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Institution: | 1. Institut für Angewandte Mathematik, Technische Universit?t Braunschweig, Pockelsstr. 14, D-38106, Braunschweig, Germany
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Abstract: | We consider errors of positive quadrature formulas applied to Chebyshev polynomials. These errors play an important role in
the error analysis for many function classes. Hunter conjectured that the supremum of all errors in Gaussian quadrature of
Chebyshev polynomials equals the norm of the quadrature formula. We give examples, for which Hunter's conjecture does not
hold. However, we prove that the conjecture is valid for all positive quadratures if the supremum is replaced by the limit
superior. Considering a fixed positive quadrature formula and the sequence of all Chebyshev polynomials, we show that large
errors are rare. |
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Keywords: | 41A55 65D30 |
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