A Brief Introduction to GAIL (Guaranteed Automatic Integration Library) Version 2.3
Event Type
TimeTuesday, July 306:30pm - 8:30pm
LocationCrystal Foyer and Crystal B
DescriptionFunction approximation, optimization, and integration are among the most
fundamental mathematical problems. They are especially challenging when
the functions in consideration fluctuate wildly in certain parts of the
domain, or if the domain is high dimensional. Development of efficient and
effective numerical algorithms for approximating the solutions to these
problems that are based on rigorous mathematical frameworks, (statistical)
error bounds, advanced sampling strategies, and careful complexity analysis
remain active research areas. The Guaranteed Automatic Integration Library
(GAIL) is our multi-year research efforts directed towards addressing the
aforementioned overarching theme. Briefly, GAIL is a free, open-source
MATLAB software package with eight main algorithms based on over a dozen
peer-reviewed publications, involving three faculty and nine doctoral
students in Illinois Tech as well as their international collaborators. The
theories behind our algorithms consider functions in cones, rather than
balls. GAIL algorithms sample data points of a given function in an
automatic, adaptive manner. Our algorithms are iterative by design, with
error bounds computed in each iteration. The solvers stop at the first
iteration where user-given tolerance is met. They are proven to have
optimal costs. We consistently employ good industrial software development
practices for GAIL such as unit tests and integration tests, searchable
online documentation, version control systems (GitHub), and agile
methodology (using Trello). Our reproducible research have demonstrated
that GAIL could outperform more established algorithms in various ways.