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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 627-648
  • MSC: Primary 65D30; Secondary 41A55
  • DOI:
  • MathSciNet review: 1010595