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A Comparison Theorem for Linear Functionals and its Application in Quadrature

  • Klaus-Jürgen Förster
Chapter
Part of the ISNM 57: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 57)

Abstract

In literature several works on the comparison of quadrature formulae can be found. Comparison theorems have been achieved in regards to the remainders of different quadrature formulae ([5], [10], [15]) as well as to the location of the nodes [1] and the size of the weights [2]. In a recently published work Locher [13] proved a comparison criterion and showed that by the help of this criterion part of the known results can be obtained. In the first chapter of this paper a comparison criterion will be given which contains Locher’s criterion. In the following three chapters three different comparison results will be provided each of which results from this comparison criterion.

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© Springer Basel AG 1982

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  • Klaus-Jürgen Förster

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