کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6931306 | 867663 | 2015 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Weighted discrete least-squares polynomial approximation using randomized quadratures
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 298, 1 October 2015, Pages 787-800
Journal: Journal of Computational Physics - Volume 298, 1 October 2015, Pages 787-800
نویسندگان
Tao Zhou, Akil Narayan, Dongbin Xiu,