June 2020
Intermediate to advanced
158 pages
4h 36m
English
Content preview from Multivariate Algorithms and Information-Based Complexity
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1 The control variate integration algorithm for multivariate functions defined at scattered data points
Jeremy Dewar
Department of Mathematics, Tulane University, New Orleans, USA
Mu Tian
Facebook, Seattle, USA
James M. Hyman
Department of Mathematics, Tulane University, New Orleans, USA
Abstract
We describe numerical studies to demonstrate the accuracy and efficiency of approximating the integral of a function over a prescribed multidimensional region using the exact integral of a control variate based on a least-squares multivariate polynomial quasiinterpolant. This control variate integration approach is shown to be effective in approximating the integral of smooth functions, where only a few function values are available. We compare ...
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