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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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Asymptotically optimal error bounds for quadrature rules of given degree
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by H. Brass PDF
Math. Comp. 61 (1993), 785-798 Request permission

Abstract:

If the quadrature rule Q is applied to the function f, then the error can in many situations be bounded by ${\rho _s}(Q){\left \| {{f^{(s)}}} \right \|_\infty }$, where ${\rho _s}(Q)$ is independent of f. We obtain the asymptotics of these numbers for the Gaussian method $Q_n^{\text {G}}\;(n = 1,2, \ldots )$ with very general weight functions and show that ${\rho _s}(Q_n^{\text {G}})$ is (asymptotically) an upper bound for ${\rho _s}(Q)$, if Q is any quadrature rule with the same degree as $Q_n^{\text {G}}$.
References
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Math. Comp. 61 (1993), 785-798
  • MSC: Primary 41A55; Secondary 65D32
  • DOI: https://doi.org/10.1090/S0025-5718-1993-1192968-8
  • MathSciNet review: 1192968