Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty

被引：5
|
作者：
Guo, Ling [1 ]
Li, Jing [2 ]
Liu, Yongle [3 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China
[2] Pacific Northwest Natl Lab, Richland, WA 99354 USA
[3] Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
来源：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2018年 / 8卷 / 03期
关键词：
Uncertainty quantification; stochastic collocation; DCA-TL1; minimisation; compressive sensing; restricted isometry property; POLYNOMIAL CHAOS; SPARSE APPROXIMATION; VARIABLE SELECTION; SIGNAL RECOVERY; ALGORITHMS;
D O I：
10.4208/eajam.060518.130618
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The sparse reconstruction of functions via a transformed l(1) (TL1) minimisation is studied and theoretical results concerning recoverability and accuracy of such reconstruction from undersampled measurements are obtained. To identify the coefficients of sparse orthogonal polynomial expansions in uncertainty quantification, the method is combined with the stochastic collocation approach. The DCA-TL1 algorithm [37] is used in implementing the TL1 minimisation. Various numerical examples demonstrate the recoverability and efficiency of this method.
引用
收藏
页码：566 / 585
页数：20
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