Abstract
This paper is concerned with numerical integration over the unit square U2 of continuous functions which are periodic in both variables. The concept of r-th order blending rectangle rule is introduced by carrying over the idea from Boolean interpolation. Error bounds are developed, and it is shown that r-th order blending rectangle rules are comparable with number-theoretic cubature rules.
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References
G. Baszenski and F.-J. Delvos Boolean methods in Fourier approximation. In “Topics in Multivariate Approximation” (C. K. Chui, L. L. Schumaker, F. Utreras, Eds. ), Academic Press 1987, 1–11.
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© 1989 Birkhäuser Verlag Basel
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Delvos, FJ. (1989). R-th Order Blending Rectangle Rules. In: Multivariate Approximation Theory IV. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7298-0_12
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DOI: https://doi.org/10.1007/978-3-0348-7298-0_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7300-0
Online ISBN: 978-3-0348-7298-0
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