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Mathematics of Computation

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

 

 

Comparison of Birkhoff type quadrature formulae


Authors: Borislav Bojanov and Geno Nikolov
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
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1990-1010595-7
Article copyright: © Copyright 1990 American Mathematical Society