TY - JOUR T1 - Stochastic Collocation via $l_1$-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification JO - East Asian Journal on Applied Mathematics VL - 2 SP - 171 EP - 191 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.090615.060216a UR - https://global-sci.org/intro/article_detail/eajam/10787.html KW - Stochastic collocation, Quasi-Monte Carlo sequence, low discrepancy point sets, Legendre polynomials, $ℓ_1$-minimisation. AB -

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.