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Title: On polynomial chaos expansion via gradient-enhanced ℓ1-minimization

Journal Article · · Journal of Computational Physics

Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
CMMI-1454601; DMS-1228359; SC0006402; CNS-0821794
OSTI ID:
1348861
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 310 Journal Issue: C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 50 works
Citation information provided by
Web of Science

References (32)

Sparse Legendre expansions via <mml:math altimg="si12.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-minimization journal May 2012
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies journal January 2015
Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution journal January 2003
User-Friendly Tail Bounds for Sums of Random Matrices journal August 2011
Orthogonal Bases for Polynomial Regression with Derivative Information in Uncertainty Quantification journal January 2011
On verifiable sufficient conditions for sparse signal recovery via ℓ 1 minimization journal October 2010
Polynomial Regression Approaches Using Derivative Information for Uncertainty Quantification journal February 2010
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information journal February 2006
On the Stability and Accuracy of Least Squares Approximations journal March 2013
Enhancing 1 -minimization estimates of polynomial chaos expansions using basis selection journal May 2015
The restricted isometry property and its implications for compressed sensing journal May 2008
A non-adapted sparse approximation of PDEs with stochastic inputs journal April 2011
A survey of cross-validation procedures for model selection journal January 2010
A weighted -minimization approach for sparse polynomial chaos expansions journal June 2014
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations journal January 2002
Compressed sensing journal April 2006
Gradient-based methods for uncertainty quantification in hypersonic flows journal October 2013
On sparse reconstruction from Fourier and Gaussian measurements journal January 2008
High-Order Collocation Methods for Differential Equations with Random Inputs journal January 2005
Reweighted minimization method for stochastic elliptic differential equations journal September 2013
Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression journal June 2015
Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators journal March 1985
The estimation of functional uncertainty using polynomial chaos and adjoint equations journal May 2010
A Probabilistic and RIPless Theory of Compressed Sensing journal November 2011
An Introduction to the Adjoint Approach to Design journal December 2000
Accuracy Guarantees for $\ell_1$-Recovery journal December 2011
STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION journal January 2012
Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces journal January 2013
Sparse pseudospectral approximation method journal July 2012
Suprema of Chaos Processes and the Restricted Isometry Property journal January 2014
A Simple Proof of the Restricted Isometry Property for Random Matrices journal January 2008
Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection journal February 2003

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