Stable High Order Quadrature Rules for Scattered Data and General Weight Functions

TL;DR

This paper introduces stable high order quadrature rules designed for scattered data and general weight functions, addressing practical challenges in numerical integration when data is irregular or difficult to fit traditional rules.

Contribution

It proposes a novel method for constructing high order quadrature rules that are stable and applicable to scattered data with arbitrary weight functions, expanding the usability of numerical integration.

Findings

Quadrature rules are stable for scattered data.

Applicable to general weight functions.

Achieves high accuracy with experimental data.

Abstract

Numerical integration is encountered in all fields of numerical analysis and the engineering sciences. By now, various efficient and accurate quadrature rules are known; for instance, Gauss-type quadrature rules. In many applications, however, it might be impractical---if not even impossible---to obtain data to fit known quadrature rules. Often, experimental measurements are performed at equidistant or even scattered points in space or time. In this work, we propose stable high order quadrature rules for experimental data, which can accurately handle general weight functions.