East Asian J. Appl. Math., 6 (2016), pp. 171-191.
Published online: 2018-02
Cited by
- BibTex
- RIS
- TXT
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.
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.