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The error norm of Clenshaw–Curtis and related quadrature formulae

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Abstract

We consider interpolatory quadrature formulae relative to the Legendre weight function \(w(t)=1\) on the interval \([-1,1]\). On certain spaces of analytic functions the error term of these formulae is a continuous linear functional. We obtain new estimates for the norm of the error functional when the latter does not keep a constant sign at the monomials. Subsequently, the derived estimates are applied into the case of the Clenshaw–Curtis formula, the Basu formula and the Fejér formula of the first kind.

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Athens, Greece

    Sotirios E. Notaris

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  1. Sotirios E. Notaris
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Correspondence to Sotirios E. Notaris.

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Communicated by Lothar Reichel.

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Notaris, S.E. The error norm of Clenshaw–Curtis and related quadrature formulae. Bit Numer Math 56, 705–728 (2016). https://doi.org/10.1007/s10543-015-0569-6

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  • DOI: https://doi.org/10.1007/s10543-015-0569-6

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