New lower bound estimates for quadratures of bounded analytic functions

TL;DR

This paper presents improved lower bounds on the error of numerical quadrature methods for integrating bounded analytic functions near the interval [-1,1], enhancing understanding of their limitations.

Contribution

It introduces tighter lower bounds for quadrature errors of analytic functions, advancing theoretical knowledge in numerical integration accuracy.

Findings

Derived new lower bounds for quadrature errors

Applicable to functions bounded in neighborhoods of [-1,1]

Improves upon previous error estimates

Abstract

We give an improved lower bound for the error of any quadrature computing $\int_{-1}^1 f(x) d\alpha(x)$ of analytic functions bounded in the neighborhood of $[-1,1]$.