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Error derivation in Romberg integration

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Abstract

The error term related to a Romberg type extrapolation scheme based on the use of an arbitrary quadrature formula is derived. A complete discussion, utilizing the known properties of the Bernoulli polynomials and their related periodic functions, is presented in the case of a repeated halving of the integration interval. The general expression for the error term is derived in the case of an arbitrary subdivision of the integration interval.

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Authors and Affiliations

  1. Institutt for Numerisk (Anvendt) Matematikk, Norges Tekniske Høgskole, Trondheim, Norway

    Tore Håvie

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  1. Tore Håvie
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Work performed while the author was working as staff member at CERN, Geneva, Switzerland.

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Håvie, T. Error derivation in Romberg integration. BIT 12, 516–527 (1972). https://doi.org/10.1007/BF01932961

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  • DOI: https://doi.org/10.1007/BF01932961

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