Author’s abstract: The problem of the best recovery in the sense of Sard of a linear functional \(Lf\) on the basis of information \(T(f)=\{L_jf,\;j=1,2,\dots,N\}\) 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 \(L(K_nK_m)\) in the space \(S=\operatorname{span}\{L_j(K_n\bar K_m),\;j=1,2,\dots,N\}\), where \(K_n(x,t)=K(x,t)-L^x_n(K(\cdot,t);x)\) 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 the blending grid are given. An algorithm is designed and realized using the software product Matlab.