On "Upper error bounds for quadrature formulas on function classes" by K. K. Frolov

TL;DR

This tutorial paper provides a complete proof of Frolov's result on the optimal convergence order of numerical integration methods for functions with bounded mixed derivatives, following Temlyakov's presentation.

Contribution

It offers a detailed, accessible proof of Frolov's theorem, clarifying the optimal convergence order for a class of functions in numerical integration.

Findings

Proves the optimal order of convergence for Frolov's quadrature.

Clarifies the theoretical foundation for numerical integration of mixed derivative functions.

Provides a comprehensive tutorial on the proof of Frolov's result.

Abstract

This is a tutorial paper that gives the complete proof of a result of Frolov [2] that shows the optimal order of convergence for numerical integration of functions with bounded mixed derivatives. The presentation follows Temlyakov [8], see also [7].