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Stochastic Collocation via l1-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification

Part of: Stochastic analysis Partial differential equations, boundary value problems Approximations and expansions

Published online by Cambridge University Press:  12 May 2016

Yongle Liu  and
Ling Guo
Yongle Liu
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai, China
Ling Guo*
Affiliation:
Department of Mathematics and E-Institute of Shanghai Universities and Scientific Computing, Shanghai Normal University, Shanghai, China
*
*Corresponding author. Email address:lguo@shnu.edu.cn (L. Guo)
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Abstract

Various numerical methods have been developed in order to solve complex systems with uncertainties, and the stochastic collocation method using l1-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 l1-minimisation.

Keywords

Stochastic collocationQuasi-Monte Carlo sequencelow discrepancy point setsLegendre polynomialsl1-minimisation

MSC classification

Secondary: 41A10: Approximation by polynomials 60H35: Computational methods for stochastic equations 65N35: Spectral, collocation and related methods
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 2 , May 2016 , pp. 171 - 191
Copyright
Copyright © Global-Science Press 2016 

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