Foucart, Simon Full recovery from point values: an optimal algorithm for Chebyshev approximability prior. (English) Zbl 1525.41001 Adv. Comput. Math. 49, No. 4, Paper No. 57, 14 p. (2023). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 41A05 41A10 41A50 90C05 PDFBibTeX XMLCite \textit{S. Foucart}, Adv. Comput. Math. 49, No. 4, Paper No. 57, 14 p. (2023; Zbl 1525.41001) Full Text: DOI arXiv
Foucart, Simon; Tadmor, Eitan; Zhong, Ming On the sparsity of Lasso minimizers in sparse data recovery. (English) Zbl 1512.94020 Constr. Approx. 57, No. 2, 901-919 (2023). MSC: 94A12 94A20 15B52 PDFBibTeX XMLCite \textit{S. Foucart} et al., Constr. Approx. 57, No. 2, 901--919 (2023; Zbl 1512.94020) Full Text: DOI arXiv
Foucart, Simon; Liao, Chunyang Optimal recovery from inaccurate data in Hilbert spaces: regularize, but what of the parameter? (English) Zbl 1528.41097 Constr. Approx. 57, No. 2, 489-520 (2023). MSC: 41A65 46N40 90C22 90C47 PDFBibTeX XMLCite \textit{S. Foucart} and \textit{C. Liao}, Constr. Approx. 57, No. 2, 489--520 (2023; Zbl 1528.41097) Full Text: DOI arXiv
Foucart, Simon; Liao, Chunyang; Shahrampour, Shahin; Wang, Yinsong Learning from non-random data in Hilbert spaces: an optimal recovery perspective. (English) Zbl 1498.46078 Sampl. Theory Signal Process. Data Anal. 20, No. 1, Paper No. 5, 19 p. (2022). MSC: 46N40 90C22 90C47 68T05 PDFBibTeX XMLCite \textit{S. Foucart} et al., Sampl. Theory Signal Process. Data Anal. 20, No. 1, Paper No. 5, 19 p. (2022; Zbl 1498.46078) Full Text: DOI arXiv
Daubechies, I.; DeVore, R.; Foucart, S.; Hanin, B.; Petrova, G. Nonlinear approximation and (deep) ReLU networks. (English) Zbl 1501.41003 Constr. Approx. 55, No. 1, 127-172 (2022). Reviewer: Peter Massopust (München) MSC: 41A25 41A30 41A46 68T07 82C32 92B20 PDFBibTeX XMLCite \textit{I. Daubechies} et al., Constr. Approx. 55, No. 1, 127--172 (2022; Zbl 1501.41003) Full Text: DOI arXiv
Ettehad, Mahmood; Foucart, Simon Instances of computational optimal recovery: dealing with observation errors. (English) Zbl 1483.41012 SIAM/ASA J. Uncertain. Quantif. 9, 1438-1456 (2021). Reviewer: Sorin-Mihai Grad (Paris) MSC: 41A65 49M29 65K05 90C22 90C47 PDFBibTeX XMLCite \textit{M. Ettehad} and \textit{S. Foucart}, SIAM/ASA J. Uncertain. Quantif. 9, 1438--1456 (2021; Zbl 1483.41012) Full Text: DOI arXiv
Foucart, Simon Instances of computational optimal recovery: refined approximability models. (English) Zbl 1460.65068 J. Complexity 62, Article ID 101503, 13 p. (2021). MSC: 65K05 90C22 PDFBibTeX XMLCite \textit{S. Foucart}, J. Complexity 62, Article ID 101503, 13 p. (2021; Zbl 1460.65068) Full Text: DOI arXiv
Ettehad, Mahmood; Foucart, Simon Approximability models and optimal system identification. (English) Zbl 1436.93031 Math. Control Signals Syst. 32, No. 1, 19-41 (2020). MSC: 93B30 93C25 30H10 PDFBibTeX XMLCite \textit{M. Ettehad} and \textit{S. Foucart}, Math. Control Signals Syst. 32, No. 1, 19--41 (2020; Zbl 1436.93031) Full Text: DOI arXiv
Foucart, Simon Sampling schemes and recovery algorithms for functions of few coordinate variables. (English) Zbl 1457.62180 J. Complexity 58, Article ID 101457, 8 p. (2020). MSC: 62H15 62F03 41A63 65D05 94A20 PDFBibTeX XMLCite \textit{S. Foucart}, J. Complexity 58, Article ID 101457, 8 p. (2020; Zbl 1457.62180) Full Text: DOI
Foucart, Simon; Gribonval, Rémi; Jacques, Laurent; Rauhut, Holger Jointly low-rank and bisparse recovery: questions and partial answers. (English) Zbl 1434.65050 Anal. Appl., Singap. 18, No. 1, 25-48 (2020). MSC: 65F50 65F55 PDFBibTeX XMLCite \textit{S. Foucart} et al., Anal. Appl., Singap. 18, No. 1, 25--48 (2020; Zbl 1434.65050) Full Text: DOI arXiv
Foucart, S.; Hielsberg, M.; Mullendore, G. L.; Petrova, G.; Wojtaszczyk, P. Optimal algorithms for computing average temperatures. (English) Zbl 1504.86011 Math. Clim. Weather Forecast. 5, 34-44 (2019). MSC: 86A10 86A32 86-08 PDFBibTeX XMLCite \textit{S. Foucart} et al., Math. Clim. Weather Forecast. 5, 34--44 (2019; Zbl 1504.86011) Full Text: DOI
Foucart, Simon; Lasserre, Jean Bernard Computation of Chebyshev polynomials for union of intervals. (English) Zbl 1436.30004 Comput. Methods Funct. Theory 19, No. 4, 625-641 (2019). MSC: 30C10 30E10 PDFBibTeX XMLCite \textit{S. Foucart} and \textit{J. B. Lasserre}, Comput. Methods Funct. Theory 19, No. 4, 625--641 (2019; Zbl 1436.30004) Full Text: DOI arXiv
DeVore, Ronald; Foucart, Simon; Petrova, Guergana; Wojtaszczyk, Przemyslaw Computing a quantity of interest from observational data. (English) Zbl 1414.41019 Constr. Approx. 49, No. 3, 461-508 (2019). Reviewer: Vasile Postolică (Piatra Neamt) MSC: 41A65 41A46 46N40 65D32 PDFBibTeX XMLCite \textit{R. DeVore} et al., Constr. Approx. 49, No. 3, 461--508 (2019; Zbl 1414.41019) Full Text: DOI
Foucart, Simon Flavors of compressive sensing. (English) Zbl 1391.94211 Fasshauer, Gregory E. (ed.) et al., Approximation theory XV: San Antonio 2016. Selected papers based on the presentations at the international conference, San Antonio, TX, USA, May 22–25, 2016. Cham: Springer (ISBN 978-3-319-59911-3/hbk; 978-3-319-59912-0/ebook). Springer Proceedings in Mathematics & Statistics 201, 61-104 (2017). MSC: 94A12 PDFBibTeX XMLCite \textit{S. Foucart}, Springer Proc. Math. Stat. 201, 61--104 (2017; Zbl 1391.94211) Full Text: DOI
Foucart, Simon; Skrzypek, Lesław On maximal relative projection constants. (English) Zbl 1371.46010 J. Math. Anal. Appl. 447, No. 1, 309-328 (2017). MSC: 46B07 46B04 52A21 PDFBibTeX XMLCite \textit{S. Foucart} and \textit{L. Skrzypek}, J. Math. Anal. Appl. 447, No. 1, 309--328 (2017; Zbl 1371.46010) Full Text: DOI
Bouchot, Jean-Luc; Foucart, Simon; Hitczenko, Pawel Hard thresholding pursuit algorithms: number of iterations. (English) Zbl 1346.65012 Appl. Comput. Harmon. Anal. 41, No. 2, 412-435 (2016). MSC: 65F10 15A29 65F50 PDFBibTeX XMLCite \textit{J.-L. Bouchot} et al., Appl. Comput. Harmon. Anal. 41, No. 2, 412--435 (2016; Zbl 1346.65012) Full Text: DOI Link
Foucart, Simon Stability and robustness of \(\ell_1\)-minimizations with Weibull matrices and redundant dictionaries. (English) Zbl 1332.94042 Linear Algebra Appl. 441, 4-21 (2014). MSC: 94A20 42C15 65K10 PDFBibTeX XMLCite \textit{S. Foucart}, Linear Algebra Appl. 441, 4--21 (2014; Zbl 1332.94042) Full Text: DOI
Foucart, Simon; Pajor, Alain; Rauhut, Holger; Ullrich, Tino The Gelfand widths of \(\ell_p\)-balls for \(0 < p \leq 1\). (English) Zbl 1204.41019 J. Complexity 26, No. 6, 629-640 (2010). MSC: 41A46 PDFBibTeX XMLCite \textit{S. Foucart} et al., J. Complexity 26, No. 6, 629--640 (2010; Zbl 1204.41019) Full Text: DOI arXiv
Foucart, S.; Kryakin, Y.; Shadrin, A. On the exact constant in the Jackson-Stechkin inequality for the uniform metric. (English) Zbl 1181.41017 Constr. Approx. 29, No. 2, 157-179 (2009). Reviewer: D. K. Ugulawa (Tbilisi) MSC: 41A17 41A44 42A10 PDFBibTeX XMLCite \textit{S. Foucart} et al., Constr. Approx. 29, No. 2, 157--179 (2009; Zbl 1181.41017) Full Text: DOI arXiv
Foucart, Simon; Lai, Ming-Jun Sparsest solutions of underdetermined linear systems via \( \ell _q\)-minimization for \(0<q\leqslant 1\). (English) Zbl 1171.90014 Appl. Comput. Harmon. Anal. 26, No. 3, 395-407 (2009). Reviewer: Gerhard-Wilhelm Weber (Ankara) with Ayşe Özmen and Özge Erdem MSC: 90C30 41A27 PDFBibTeX XMLCite \textit{S. Foucart} and \textit{M.-J. Lai}, Appl. Comput. Harmon. Anal. 26, No. 3, 395--407 (2009; Zbl 1171.90014) Full Text: DOI