Boolean Methods for Double Integration
Franz-J. Delvos · Mathematics of Computation · 1990
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.