Stochastic Collocation Methods via Minimisation of the Transformed L-1-Penalty

Guo, Ling1; Li, Jing2; Liu, Yongle3

2018-08

10.4208/eajam.060518.130618

East Asian Journal on Applied Mathematics   影响因子和分区

2079-7362

2079-7370

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.

Uncertainty quantification stochastic collocation DCA-TL1 minimisation compressive sensing restricted isometry property

SCI

英语

其他

Program for Outstanding Academic leaders in Shanghai City[151503100]

Mathematics

Mathematics, Applied

WOS:000456113000012

GLOBAL SCIENCE PRESS

Web of Science

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

Guo, Ling,Li, Jing,Liu, Yongle. Stochastic Collocation Methods via Minimisation of the Transformed L-1-Penalty[J]. East Asian Journal on Applied Mathematics,2018,8(3):566-585.

Guo, Ling,Li, Jing,&Liu, Yongle.(2018).Stochastic Collocation Methods via Minimisation of the Transformed L-1-Penalty.East Asian Journal on Applied Mathematics,8(3),566-585.

Guo, Ling,et al."Stochastic Collocation Methods via Minimisation of the Transformed L-1-Penalty".East Asian Journal on Applied Mathematics 8.3(2018):566-585.