Stochastic Collocation via $l_1$-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification
Year: 2016
East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 2 : pp. 171–191
Abstract
Various numerical methods have been developed in order to solve complex
systems with uncertainties, and the stochastic collocation method using $ℓ_1$-
minimisation on low discrepancy point sets is investigated here. Halton and Sobol’ sequences are considered, and low discrepancy point sets and random points are
compared. The tests discussed involve a given target function in polynomial form,
high-dimensional functions and a random ODE model. Our numerical results
show that the low discrepancy point sets perform as well or better than random
sampling for stochastic collocation via $ℓ_1$-minimisation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.090615.060216a
East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 2 : pp. 171–191
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Stochastic collocation Quasi-Monte Carlo sequence low discrepancy point sets Legendre polynomials $ℓ_1$-minimisation.