TY - JOUR
T1 - Stochastic Collocation via $l_1$-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification
AU - Yongle Liu & Ling Guo
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 - <p style="text-align: justify;">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.<br/></p>