Linear algorithms with finite deviation (Q1265140)

The paper is devoted to the problem of computing the positive functional \(I\) on \(C[a,b ]\) which makes use of function values \((f(x_1),f(x_2),\dots,f(x_n))\) and the more global information of \(f\) belonging to a given set \(K \in C[a,b ]\). A strongly optimal algorithm which makes the fullest use of the input information is studied. It is shown that the studied algorithms in many cases are nonlinear in contradiction to optimal ones. A weakening of the notion of strong optimality leads to algorithms with finite deviation for which almost the same results are obtained. Some examples of linear algorithms with small deviation are given.