Approximations of certain classes of functions of several variables by greedy approximants in the integral metrics

TL;DR

This paper derives precise estimates for how well certain multivariable functions can be approximated using greedy algorithms and best n-term orthogonal trigonometric methods in integral metrics.

Contribution

It provides the exact order estimates for function approximation errors of specific classes using greedy and orthogonal trigonometric methods in the integral metric.

Findings

Exact order estimates for greedy approximations.

Exact order estimates for best n-term orthogonal trigonometric approximations.

Results apply to classes of functions of several variables.

Abstract

We find the exact order estimates of the approximations of the classes ${\cal F}_{q,r}^{\psi}$ of functions of several variables by greedy approximants in the integral metric. We also obtain the exact order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q,r}^{\psi}$ in the integral metric.