full
search.png

Search

close.png

Cancel

arrow
Volume 8, Issue 3
Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty

Ling Guo, Jing Li & Yongle Liu

DOI: 10.4208/eajam.060518.130618

East Asian J. Appl. Math., 8 (2018), pp. 566-585.

Published online: 2018-08

Preview Purchase PDF 2194 32100

Cited by

google scholar semantic scholar
Export citation
  • Abstract

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.

  • Keywords

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

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-8-566, author = {Ling Guo, Jing Li and Yongle Liu}, title = {Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {3}, pages = {566--585}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.060518.130618}, url = {http://global-sci.org/intro/article_detail/eajam/12626.html} }
TY - JOUR T1 - Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty AU - Ling Guo, Jing Li & Yongle Liu JO - East Asian Journal on Applied Mathematics VL - 3 SP - 566 EP - 585 PY - 2018 DA - 2018/08 SN - 8 DO - http://doi.org/10.4208/eajam.060518.130618 UR - https://global-sci.org/intro/article_detail/eajam/12626.html KW - Uncertainty quantification, stochastic collocation, DCA-TL1 minimisation, compressive sensing, restricted isometry property. AB -

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.

Ling Guo, Jing Li and Yongle Liu. (2018). Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty. East Asian Journal on Applied Mathematics. 8 (3). 566-585. doi:10.4208/eajam.060518.130618
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard