Subsampled Gauss Quadrature Nodes for Estimating Polynomial Chaos Expansions
Subsampled Gauss Quadrature Nodes for Estimating Polynomial Chaos Expansions
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DOI：
10.1137/130913511
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
Gary Tang;G. Iaccarino
中科院分区：
文献类型：
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作者：
Gary Tang;G. Iaccarino
将压缩传感的原理应用于不确定性量化问题有很大的兴趣。一个这样的问题是近似的L^2 $随机过程使用广义多项式混沌展开。也就是说，它提供了一种新的方法来估计的扩展时，随机过程是一个函数的大量随机变量。本文介绍了一种新的估计程序的勒让德多项式展开，在压缩感知形式主义，随机采样的高斯求积规则定义的点集。我们在非渐近制度的误差估计和相关的结果切比雪夫采样的正交点的数量$n\\infty$。最后，我们比较其在现实世界中的表现，在文献中的其他采样方案。
There is a great deal of interest in applying the principles of compressed sensing to problems in uncertainty quantification. One such problem is the approximation of $L^2$ stochastic processes using generalized polynomial chaos expansions. Namely, it presents a new approach to estimating the expansions when the stochastic process is a function of a large number of random variables. This paper describes a new estimation procedure for the Legendre polynomial expansion, within the compressed sensing formalism, by randomly sampling from the set of points defined by Gauss quadrature rules. We give error estimates in the nonasymptotic regime and relate the results to Chebyshev sampling as the number of quadrature points $n\to\infty$. Finally, we compare its real-world performance to other sampling schemes in the literature.