The problem of the best recovery in the sense of Sard of a linear functional Lf on the basis of information T(f) = {Ljf,j = 1, 2,... N} is studied. It is shown that in the class of bivariate functions with restricted (n,m) -derivative, known on the (n,m)-grid lines, the problem of the best recovery of a linear functional leads to the best approximation of L(KnKm) in the space S = span Lj(Kn_Km), j=1; 2,...N}, where Kn(x,t) = K(x,t)- Lxn(K(.,t):x) is the difference between the truncated power kernel K(x,t) = (x-t)n-1+ =(n-1)! and its Lagrange interpolation formula. In particular, the best recovery of a bivariate function is considered, if scattered data points and blending grid are given. An algorithm is designed and realized using the software product MATLAB.
On some consequences which follow from the Lagrange interpolation formula