Volume 58, pp. 582-596, 2023.

An optimal method for recovering the mixed derivative $f^{(2,2)}$ of bivariate functions

Y. V. Semenova and S. G. Solodky

Abstract

The problem of recovering the mixed derivative $f^{(2,2)}$ for bivariate functions is investigated. Based on the truncation method, a numerical differentiation algorithm is constructed that uses perturbed Fourier–Legendre coefficients of the function as input information. Moreover, the idea of a hyperbolic cross is implemented, which makes it possible to significantly reduce computational costs. It is established that this algorithm guarantees order-optimal accuracy (in the power scale) with a minimal amount of Galerkin information involved.

Full Text (PDF) [302 KB], BibTeX , DOI: 10.1553/etna_vol58s582

Key words

numerical differentiation, Legendre polynomials, truncation method, information complexity, optimal error estimates

AMS subject classifications

47A52, 65D25