TY - JOUR
T1 - Stochastic Collocation Methods via Minimisation of the Transformed L<sub>1</sub>-Penalty
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 - <p style="text-align: justify;">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.<br/></p>