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Numerical Computation with Functions Instead of Numbers

Final Report Summary - FUNCOMP (Numerical Computation with Functions Instead of Numbers)

Summary of achievements
This research project succeeded beyond expectations. All the main goals were achieved and more. Outputs included two books, three conferences, about 30 articles in top journals, about 140 research talks at various universities and other venues, and the tremendous advance of the open-source software system Chebfun, which has thousands of users and about 700 citations so far at Google Scholar. Areas of research progress included:
(1) Algorithms, software, and analysis for computing with functions in multiple dimensions,
(2) Advances in algorithms for differential equations and the new book Exploring ODEs,
(3) New “AAA algorithm” for adaptive approximation by rational functions,
(4) Steps toward a foundation for floating point arithmetic for functions,
(5) New analysis and algorithms for computation with periodic functions,
(6) New links between quadrature formulas, integrals, and applications.
The last of these topics includes a computational approach to stochastics via “smooth random functions” and, in an unexpected development, the first mathematical analysis of shielding by a Faraday cage.