About optimization of methods for mixed derivatives of bivariate functions

TL;DR

This paper develops an order-optimal numerical differentiation algorithm for high-order mixed derivatives of bivariate functions with finite smoothness, balancing accuracy and information use.

Contribution

It introduces a truncation-based method that achieves optimality in both accuracy and Galerkin information efficiency for mixed derivatives.

Findings

Algorithm is order-optimal in accuracy

Algorithm minimizes Galerkin information use

Applicable to functions with finite smoothness

Abstract

The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. On the basis of the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information.