@Article{EAJAM-6-171,
author = {Yongle Liu and Ling Guo},
title = {Stochastic Collocation via $l_1$-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {6},
number = {2},
pages = {171--191},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.090615.060216a},
url = {http://global-sci.org/intro/article_detail/eajam/10787.html}
}