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Boolean methods for double integration


Author: Franz-J. Delvos
Journal: Math. Comp. 55 (1990), 683-692
MSC: Primary 65D32
DOI: https://doi.org/10.1090/S0025-5718-1990-1035928-7
MathSciNet review: 1035928
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Abstract: This paper is concerned with numerical integration of continuous functions over the unit square $ {U^2}$. The concept of the rth-order blending rectangle rule is introduced by carrying over the idea from Boolean interpolation. Error bounds are developed, and it is shown that rth-order blending rectangle rules are comparable with number-theoretic cubature rules. Moreover, rthorder blending midpoint rules are defined and compared with the rth-order blending rectangle rules.


References [Enhancements On Off] (What's this?)

  • [1] G. Baszenski and F.-J. Delvos, Boolean methods in Fourier approximation, Topics in Multivariate Approximation (C. K. Chui, L. L. Schumaker, and F. Utreras, eds.), Academic Press, 1987, pp. 1-11. MR 924818 (88m:42010)
  • [2] F.-J. Delvos, d-variate Boolean interpolation, J. Approx. Theory 34 (1982), 99-114. MR 647256 (83b:41004)
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1990-1035928-7
Keywords: Multiple integration, blending methods
Article copyright: © Copyright 1990 American Mathematical Society

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