Stochastic collocation methods via L_1 minimization using randomized quadratures [article]

Ling Guo, Akil Narayan, Tao Zhou, Yuhang Chen
2016 arXiv   pre-print
In this work, we discuss the problem of approximating a multivariate function via ℓ_1 minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points. The independent variables of the function are assumed to be random variables, and thus, the framework provides a non-intrusive way to construct the generalized polynomial chaos expansions, stemming from the motivating application of Uncertainty Quantification (UQ). We provide theoretical analysis on the
more » ... dity of the approach. The framework includes both the bounded measures such as the uniform and the Chebyshev measure, and the unbounded measures which include the Gaussian measure. Several numerical examples are given to confirm the theoretical results.
arXiv:1602.00995v2 fatcat:75pfrhgz7jcxnlu6uae7pnvnhm