GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1
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.
Cite
@article{arxiv.1503.06544,
title = {GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1},
author = {Sou-Cheng T. Choi and Yuhan Ding and Fred J. Hickernell and Lan Jiang and Lluís Antoni Jiménez Rugama and Xin Tong and Yizhi Zhang and Xuan Zhou},
journal= {arXiv preprint arXiv:1503.06544},
year = {2015}
}