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The algebraic method in quadrature for uncertainty quantification

Ko, Jordan and Wynn, Henry P. (2016) The algebraic method in quadrature for uncertainty quantification. SIAM/ASA Journal on Uncertainty Quantification, 4 (1). pp. 331-357. ISSN 2166-2525

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Identification Number: 10.1137/140978612


A general method of quadrature for uncertainty quantification (UQ) is introduced based on the algebraic method in experimental design. This is a method based on the theory of zero-dimensional algebraic varieties. It allows quadrature of polynomials or polynomial approximands for quite general sets of quadrature points, here called “designs.” The method goes some way to explaining when quadrature weights are nonnegative and gives exact quadrature for monomials in the quotient ring defined by the algebraic method. The relationship to the classical methods based on zeros of orthogonal polynomials is discussed, and numerical comparisons are made with methods such as Gaussian quadrature and Smolyak grids. Application to UQ is examined in the context of polynomial chaos expansion and the probabilistic collocation method, where solution statistics are estimated.

Item Type: Article
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Additional Information: © 2016 Society for Industrial and Applied Mathematics and American Statistical Association
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Date Deposited: 16 May 2016 11:46
Last Modified: 20 Jul 2021 02:31

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