Showing papers by "Fred J. Hickernell published in 2015"
TL;DR: In this paper, a reproducing kernel Banach space (RKBS) is introduced to solve support vector machines in the orthogonality of semi-inner products of RKBSs, which can obtain the finite-dimensional representations of the dual elements of support vector machine solutions.
39 citations
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TL;DR: The 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, and employs the best practices in mathematical research and software engineering known to us and available in MATLAB.
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.
11 citations