Guaranteed Automatic Integration Library (GAIL): An Open-Source MATLAB Library for Function Approximation, Optimization, and Integration

Abstract

Function approximation, integration, and optimization are three fundamental mathematical problems. They are especially challenging when the functions involved fluctuate wildly in certain parts of the domain, or if the domain is high dimensional. Ideally, algorithms to solve these problems should possess a rigorous mathematical framework, data-based (probabilistic) error bounds, and advanced sampling strategies for efficiency.