Boolean methods for double integration
Math. Comp. 55 (1990), 683-692
Full-text PDF Free Access
Similar Articles |
Abstract: This paper is concerned with numerical integration of continuous functions over the unit square . 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.
Baszenski and F.-J.
Delvos, Boolean methods in Fourier approximation, Topics in
multivariate approximation (Santiago, 1986) Academic Press, Boston, MA,
1987, pp. 1–12. MR 924818
Delvos, 𝑑-variate Boolean interpolation, J. Approx.
Theory 34 (1982), no. 2, 99–114. MR 647256
Delvos and H.
Posdorf, 𝑛-th order blending, Constructive theory of
functions of several variables (Proc. Conf., Math. Res. Inst., Oberwolfach,
1976) Springer, Berlin, 1977, pp. 53–64. Lecture Notes in
Math., Vol. 571. MR 0487203
Keng Hua and Yuan
Wang, Applications of number theory to numerical analysis,
Springer-Verlag, Berlin-New York; Kexue Chubanshe (Science Press), Beijing,
1981. Translated from the Chinese. MR 617192
H. Sloan, Lattice methods for multiple integration,
Proceedings of the international conference on computational and applied
mathematics (Leuven, 1984), 1985, pp. 131–143. MR 793949
- 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)
- F.-J. Delvos, d-variate Boolean interpolation, J. Approx. Theory 34 (1982), 99-114. MR 647256 (83b:41004)
- F.-J. Delvos and H. Posdorf, N-th order blending, Constructive Theory of Functions of Several Variables (W. Schempp and K. Zeller, eds.), Lecture Notes in Math., vol. 571, Springer-Verlag, 1977, pp. 53-64. MR 0487203 (58:6863)
- Hua Loo Keng and Wang Yuan, Applications of number theory to numerical analysis, Springer-Verlag, 1981. MR 617192 (83g:10034)
- I. H. Sloan, Lattice methods for multiple integration, J. Comput. Appl. Math. 12-13 (1985), 131-143. MR 793949 (86f:65045)
Retrieve articles in Mathematics of Computation
Retrieve articles in all journals
© Copyright 1990
American Mathematical Society