Abstract
Product branches of Peano kernels are used to obtain results suitable for numer-ical integration. In particular, identities and inequalities are obtained involving evaluations at an interior and at the end points. It is shown how previous work and rules in numerical integration are recaptured as particular instances of the current development. Explicit a priori bounds are provided allowing the determination of the partition required for achieving a prescribed error tolerance. In the main, Ostrowski-Grüss type inequalities are used to obtain bounds on the rules in terms of a variety of norms.
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Cerone, P. (2002). Product Branched Peano Kernels and Numerical Integration. In: Dragomir, S.S., Rassias, T.M. (eds) Ostrowski Type Inequalities and Applications in Numerical Integration. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2519-4_4
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DOI: https://doi.org/10.1007/978-94-017-2519-4_4
Publisher Name: Springer, Dordrecht
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