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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

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  • 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

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@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
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