Composite quadratures for functions of dominated variation

Abstract

We analyze the performance of the closed Newton-Cotes quadratures applied to integrands of low continuity. Order of convergence rates are obtained by dominating with a summable function the total variation of a suitable derivative of the integrand over a sequence of expanding intervals. The analysis given allows any finite number of singularities anywhere in the interval of integration.

Keywords:

• Composite quadratures
• variational seminorms
• total variation

AMS(MOS)::

• 41A55