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arXiv · 1603.03945

On the Petras algorithm for verified integration of piecewise analytic functions

Małgorzata Moczurad·Piotr Zgliczyński
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Abstract

We consider the algorithm for verified integration of piecewise analytic functions given by Petras. The analysis of the algorithm contained in Patras' paper is limited to a narrow class of functions and gives upper bounds only. We present an estimation of the complexity (measured by a number of evaluations of an integrand) of the algorithm, both upper and lower bounds, for a wider class of functions. We show examples with complexity $\Theta(|\ln\eps|/\eps^{p-1})$, for any $p >1$, where $\eps$ is the desired accuracy of the computed integral.

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Małgorzata Moczurad, Piotr Zgliczyński. 2016-03-12. On the Petras algorithm for verified integration of piecewise analytic functions. https://arxiv.org/abs/1603.03945

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