Derivation of explicit expressions for the error terms in the ordinary and the modified Romberg algorithms

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1969 English Publisher:Springer Science and Business Media LLCJournal:BIT, volume 9, pages 18-29 (issn: 0006-3835, eissn: 1572-9125,

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Authors: Havie, T.;

doi: 10.1007/bf01933536

Derivation of explicit expressions for the error terms in the ordinary and the modified Romberg algorithms

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Abstract

It is proved that the error terms for both the ordinary and the modified Romberg algorithms may be expressed in terms of Bernoulli polynomials and their related periodic functions. The properties of the error terms may thus be described using the known properties of the Bernoulli polynomials and functions.

Related Organizations

European Organization for Nuclear Research
Switzerland

Keywords

numerical analysis

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