scholarly journals Analytic regularity and stochastic collocation of high-dimensional Newton iterates

2020 ◽  
Vol 46 (3) ◽  
Author(s):  
Julio E. Castrillón-Candás ◽  
Mark Kon
Keyword(s):  
High Dimensional ◽  
Stochastic Collocation ◽  
Analytic Regularity

Stochastic Collocation vial1-Minimisation on Low Discrepancy Point Sets with Application to Uncertainty Quantification

2016 ◽  
Vol 6 (2) ◽  
pp. 171-191 ◽  
Author(s):  
Yongle Liu ◽  
Ling Guo
Keyword(s):  
Numerical Methods ◽  
Complex Systems ◽  
Collocation Method ◽  
Random Sampling ◽  
Target Function ◽  
High Dimensional ◽  
Stochastic Collocation ◽  
Point Sets ◽  
Ode Model ◽  
Better Than

AbstractVarious numerical methods have been developed in order to solve complex systems with uncertainties, and the stochastic collocation method usingl1-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 vial1-minimisation.

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