Boolean methods for double integration
Math. Comp. 55 (1990), 683-692
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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.
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