Convergence of Newton-Cotes quadratures for analytic functions |
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| Authors: | M. M. Chawla |
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| Affiliation: | (1) Department of Computer Science, University of Illinois, 61801 Urbana, Illinois, U.S.A. |
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| Abstract: | We determine (Theorem 3) the smallest closed region, containing the interva of integration, such that the analyticity of the integrand in this closed region implies the convergence of the Newton-Cotes quadratures. By considering, in particular, certain ellipses as regions of analyticity, we obtain (Theorem 4) an improvement of Davis' result on the convergence of Newton-Cotes quadratures for analytic functions. |
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