SOMOGYI ILDIKO

Abstract. We introduce the definition of the almost optimal efficiency of the cubature formulas obtained with the tensor product and boolean-sum of the numerical quadrature operators, and we also give some applications and examples for such formulas. The purpose of this note is to study the cubature formulas from efficiency point of view. We will consider the case when we have a rectangular domain and the cubature formula is constructed with the boolean-sum and tensor product of the one dimensional approximation operators. We will give the definition of the almost optimal formulas with regard to the efficiency and also some examples. Let be f a function defined and integrable on the rectangular domain Dn = [a1, b1]× [a2, b2] ×... × [an, bn] and n a rectangular partition of the domain Dn: n = ∆x1× ∆x2 ×...×∆xn, where ∆xk = {xk,1,..., xk,mk} with ak ≤ xk,1 <... < xk,mk ≤ bk. First of all we will consider the tensor product cubature formula∫ D f(x1,..., xn)dx1...dxn = ∫ b1 a1 ∫ bn an f(x1,..., xn)dx1...dxn = = Q11...Q