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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Comparison of Birkhoff type quadrature formulae
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by Borislav Bojanov and Geno Nikolov PDF
Math. Comp. 54 (1990), 627-648 Request permission

Abstract:

The classical approach to the theory of quadrature formulae is based on the concept of algebraic degree of precision (ADP). A quadrature formula ${Q_1}$ is considered to be "better" than ${Q_2}$ if ${\text {ADP}}({Q_1}) > {\text {ADP}}({Q_2})$. However, there are many quadratures that use the same number of evaluations of the integrand and have the same ADP. Then, how should one compare such formulae? We show in this paper that the error of the quadrature depends monotonically on the type of data used. Roughly speaking, the lower the order of the derivatives used, the smaller is the error. As a consequence of the main result we demonstrate the existence of Birkhoff quadrature formulae of double precision.
References
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 627-648
  • MSC: Primary 65D30; Secondary 41A55
  • DOI: https://doi.org/10.1090/S0025-5718-1990-1010595-7
  • MathSciNet review: 1010595