On Euler-Maclaurin formula

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• 作者：Franç ; ois Dubeau ^{francois.dubeau@usherbrooke.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65B15 ; 65D30 ; 41A55
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：649-660
• 全文大小：397 K

文摘

We use a simple approach to show that an Euler–Maclaurin like formula can be associated to any interpolatory quadrature rule. This result is obtained by successively adding correcting terms that are exact for polynomials of increasing degree. A decomposition of the coefficients of the Euler–Maclaurin formula in terms of the integral to compute and representations of powers of the nodes is pointed out. Optimal truncation error bounds are also obtained.