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Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas

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Abstract

We study two criteria to evaluate quadrature formulas when used in automatic quadrature programs. The former consists of the computation of a quantity depending on both the truncation error behavior and the geometric properties of the nodes of the rule. This measure allows estimating the asymptotical computational cost in various abstract models of automatic quadrature. The latter is a testing technique which can be used to measure the efficiency of the formulas under consideration in a real environment. The relationships between the two criteria are investigated and the two approaches seem in good agreement.

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Authors and Affiliations

  1. IEI-CNR, via S. Maria 46, I-56100, Pisa, Italy

    Paola Favati

  2. Dipartimento di Matematica, University of Parma, Via D'Azeglio 85/a, Parma, Italy

    Grazia Lotti

  3. Dipartamento di Informatica, University of Pisa, Corso Italia, I-56100, Pisa, Italy

    Francesco Romani

Authors
  1. Paola Favati
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  2. Grazia Lotti
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  3. Francesco Romani
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Additional information

Work supported by CNR, Grant No. 93.00570.CT01.

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Favati, P., Lotti, G. & Romani, F. Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas. BIT 34, 546–557 (1994). https://doi.org/10.1007/BF01934267

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  • DOI: https://doi.org/10.1007/BF01934267

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