Talk:Newton-Cotes formulas

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In the beginning of the article it is stated that an exponentially increasing error may occur as n increases due to Runge's phenomenon. However, this should not be the case. Runge's phenomenon relates to using an increasingly higher-order polynomial approximation. For a fixed Newton-Cotes formula (e.g., Simpson's 3/8 rule), the order of the approximating polynominal is fixed. As n increases it is the step size h that is decreasing.

Elee1l5 19:00, 1 December 2006 (UTC)

The n referred to the order of the approximating polynomial. You're thinking of composite rules, which are discussed further down. However, you have a good point that the text is confusing. I tried to improve it. I also moved that part out of the first paragraph; I don't think it's that important because high-order quadrature formulas are not used very often. -- Jitse Niesen (talk) 02:14, 2 December 2006 (UTC)

After thinking it over, I'm backtracking about it being not so important. Actually, even for order 8 (which is definitely used in practice), Gaussian quadrature has clearly lower error than Newton-Cotes. -- Jitse Niesen (talk) 12:13, 3 December 2006 (UTC)

Thanks a lot for the improvement - the text is now more clear regarding the meaning of n and the use of composite rules to avoid the catastrophic interpolation effect.

Elee1l5 17:27, 5 December 2006 (UTC)