DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1247014
Grant/Contract Number:  
SC0006402; DMS-1228359; CMMI-1201207
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Name: Journal of Computational Physics Journal Volume: 280 Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Hampton, Jerrad, and Doostan, Alireza. Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2014.09.019.
Hampton, Jerrad, & Doostan, Alireza. Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies. United States. https://doi.org/10.1016/j.jcp.2014.09.019
Hampton, Jerrad, and Doostan, Alireza. Thu . "Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies". United States. https://doi.org/10.1016/j.jcp.2014.09.019.
@article{osti_1247014,
title = {Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies},
author = {Hampton, Jerrad and Doostan, Alireza},
abstractNote = {},
doi = {10.1016/j.jcp.2014.09.019},
journal = {Journal of Computational Physics},
number = C,
volume = 280,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2014.09.019

Citation Metrics:
Cited by: 123 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A Compressed Sensing Approach for Partial Differential Equations with Random Input Data
journal, October 2012


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


Asymptotic forms for Laguerre polynomials
journal, February 1970


Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
journal, February 2006

  • Candes, E.J.; Romberg, J.; Tao, T.
  • IEEE Transactions on Information Theory, Vol. 52, Issue 2, p. 489-509
  • DOI: 10.1109/TIT.2005.862083

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

  • Arlot, Sylvain; Celisse, Alain
  • Statistics Surveys, Vol. 4, Issue 0
  • DOI: 10.1214/09-SS054

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


Mean Convergence of Expansions in Laguerre and Hermite Series
journal, July 1965

  • Askey, Richard; Wainger, Stephen
  • American Journal of Mathematics, Vol. 87, Issue 3
  • DOI: 10.2307/2373069

Atomic Decomposition by Basis Pursuit
journal, January 1998

  • Chen, Scott Shaobing; Donoho, David L.; Saunders, Michael A.
  • SIAM Journal on Scientific Computing, Vol. 20, Issue 1, p. 33-61
  • DOI: 10.1137/S1064827596304010

From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
journal, February 2009

  • Bruckstein, Alfred M.; Donoho, David L.; Elad, Michael
  • SIAM Review, Vol. 51, Issue 1, p. 34-81
  • DOI: 10.1137/060657704

Dimensionality Reduction for Complex Models via Bayesian Compressive Sensing
journal, January 2014


Probing the Pareto Frontier for Basis Pursuit Solutions
journal, January 2009

  • van den Berg, Ewout; Friedlander, Michael P.
  • SIAM Journal on Scientific Computing, Vol. 31, Issue 2
  • DOI: 10.1137/080714488

Atomic Decomposition by Basis Pursuit
journal, January 2001


Reweighted minimization method for stochastic elliptic differential equations
journal, September 2013


Adaptive sparse polynomial chaos expansion based on least angle regression
journal, March 2011


Asymptotic analysis of the Hermite polynomials from their differential–difference equation
journal, December 2007


Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials
journal, March 1994

  • Nevai, Paul; Erdélyi, Tamás; Magnus, Alphonse P.
  • SIAM Journal on Mathematical Analysis, Vol. 25, Issue 2
  • DOI: 10.1137/S0036141092236863

Multi-resolution analysis of Wiener-type uncertainty propagation schemes
journal, July 2004

  • Le Maı̂tre, O. P.; Najm, H. N.; Ghanem, R. G.
  • Journal of Computational Physics, Vol. 197, Issue 2
  • DOI: 10.1016/j.jcp.2003.12.020

A Probabilistic and RIPless Theory of Compressed Sensing
journal, November 2011

  • Candes, Emmanuel J.; Plan, Yaniv
  • IEEE Transactions on Information Theory, Vol. 57, Issue 11
  • DOI: 10.1109/TIT.2011.2161794

STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION
journal, January 2012


Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
journal, January 2004


Monte Carlo sampling methods using Markov chains and their applications
journal, April 1970


Sparse Multiresolution Regression for Uncertainty Propagation
journal, January 2014


“Coarse” stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples
journal, June 2002

  • Makeev, Alexei G.; Maroudas, Dimitrios; Kevrekidis, Ioannis G.
  • The Journal of Chemical Physics, Vol. 116, Issue 23
  • DOI: 10.1063/1.1476929