GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1

TL;DR

GAIL is an open-source MATLAB library designed for reliable, adaptive, and guaranteed numerical integration, approximation, and optimization, emphasizing reproducibility and robust scientific software practices.

Contribution

This paper introduces GAIL, a comprehensive MATLAB package that provides guaranteed adaptive algorithms for integration, approximation, and optimization with a focus on reproducibility.

Findings

Provides reliable one-dimensional and multidimensional integration methods.

Includes adaptive algorithms with guaranteed accuracy.

Supports reproducible scientific computing practices.

Abstract

Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-source MATLAB package, Guaranteed Automatic Integration Library (GAIL), following the philosophy of reproducible research and sustainable practices of robust scientific software development. For our conviction that true scholarship in computational sciences are characterized by reliable reproducibility, we employ the best practices in mathematical research and software engineering known to us and available in MATLAB. This document describes the key features of functions in GAIL, which includes one-dimensional function approximation and minimization using linear splines, one-dimensional numerical integration using trapezoidal rule, and last but not least, mean estimation and multidimensional integration by Monte Carlo methods or Quasi Monte Carlo methods.