Optimal Methods for Recovering Mixed Derivatives of Non-Periodic Functions

The problem of numerical differentiation for non-periodic bivariate functions is investigated. For the recovering mixed derivatives of such functions an approach on the base of truncation method is proposed. The constructed algorithms deal with Legendere polynomials, the degree of which is chosen so as to minimize the approximation error. It is established that these algorithms are order-optimal both in terms of accuracy and in the sense of the amount of Galerkin information involved.