@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 = {
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.