Summary
Several familiar criteria used to specify and classify numerical quadrature rules for the hypercube are compared. The discussion is based on two series for the error functional, these being generalizations of the Euler Maclaurin asymptotic expansion and the Poisson Summation Formula, respectively. Topics include algebraic and trigonometric degree, Romberg Integration, and the criteria for “Good Lattice” rules. This paper is solely concerned with solidifying known theory. No new results are given here.
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© 1988 Springer Basel AG
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Lyness, J.N. (1988). Some Comments on Quadrature Rule Construction Criteria. In: Braß, H., Hämmerlin, G. (eds) Numerical Integration III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 85. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6398-8_12
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DOI: https://doi.org/10.1007/978-3-0348-6398-8_12
Publisher Name: Birkhäuser, Basel
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