Stochastic collocation methods via L₁ minimization using randomized quadratures

2016/02/02 by Ling Guo, Guo, Ling, Narayan, Akil +4 · 1 citation
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Scientific Research and Discoveries #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1602.00995

openalex publication_date 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we discuss the problem of approximating a multivariate function via ℓ₁ 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 validity 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.

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