The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
A non-adapted sparse approximation of PDEs with stochastic inputs
Open accessAbstract
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.909319 · Cited by 2,064 · cited 1×
“Numerous solvers based on the active set [54,36], interior-point continuation [21,42] and projected gradient [25,23,39,13,9,62,3,4] methods have been developed for solving the above formulations of the ‘1-minimization problem.”
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POLYNOMIAL-CHAOS-BASED KRIGING
Schobi, R., Sudret, B., & Wiart, J. (2015) · International Journal for Uncertainty Quantification · doi:10.1615/int.j.uncertaintyquantification.2015012467 · Cited by 398
Metadata
- Authors
- Doostan, A., & Owhadi, H.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2011-04
- Volume
- 230
- Issue
- 8
- Pages
- 3015-3034
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W2056558085
- Cited by
- 436
- References
- 3
- FWCI
- 20.94
- Type
- journal article
- Language
- en
- Open access
- green
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