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Quadrature rules with (not too many) derivatives (1109.0326v1)
Published 1 Sep 2011 in math.CA and math.NA
Abstract: Quadrature formulas for $\int_ab f(x) dx$ where derivative terms need only be evaluated at $a$ and $b$ in the composite rule are identified. Error bounds are given when $f:[a,b]\to\mathbb{R}$ satisfies $f{(n-1)}$ is absolutely continuous so that $f{(n)}\in Lp([a,b])$, and when $f{(n-1)}$ is merely continuous.