Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.060518.130618
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 566–585
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Uncertainty quantification stochastic collocation DCA-TL1 minimisation compressive sensing restricted isometry property.
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