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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 2024 MCQ for Mathematics of Computation is 1.78.

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A note on extended Gaussian quadrature rules
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by Giovanni Monegato PDF
Math. Comp. 30 (1976), 812-817 Request permission

Abstract:

Extended Gaussian quadrature rules of the type first considered by Kronrod are examined. For a general nonnegative weight function, simple formulas for the computation of the weights are given, together with a condition for the positivity of the weights associated with the new nodes. Examples of nonexistence of these rules are exhibited for the weight functions $(1-x^2)^{\lambda - 1/2}$, $e^{-x^2}$ and $e^{-x}$. Finally, two examples are given of quadrature rules which can be extended repeatedly.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 812-817
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0440878-3
  • MathSciNet review: 0440878