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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Error bounds for Gauss-Kronrod quadrature formulae
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by Sven Ehrich PDF
Math. Comp. 62 (1994), 295-304 Request permission

Abstract:

The Gauss-Kronrod quadrature formula $Q_{2n + 1}^{GK}$, is used for a practical estimate of the error $R_n^G$ of an approximate integration using the Gaussian quadrature formula $Q_n^G$. Studying an often-used theoretical quality measure, for $Q_{2n + 1}^{GK}$ we prove best presently known bounds for the error constants \[ {c_s}(R_{2n + 1}^{GK}) = \sup \limits _{{{\left \| {{f^{(s)}}} \right \|}_\infty } \leq 1} |R_{2n + 1}^{GK}[f]|\] in the case $s = 3n + 2 + \kappa ,\kappa = \left \lfloor {\frac {{n + 1}}{2}} \right \rfloor - \left \lfloor {\frac {n}{2}} \right \rfloor$. A comparison with the Gaussian quadrature formula $Q_{2n + 1}^G$ shows that there exist quadrature formulae using the same number of nodes but having considerably better error constants.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 62 (1994), 295-304
  • MSC: Primary 65D32; Secondary 41A55
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1208221-0
  • MathSciNet review: 1208221