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Stochastic Collocation via $l_1$-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification

Stochastic Collocation via $l_1$-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification
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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.

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