Recent Publications
2020
 (B. Hanin and G. Petrova), Neural Network Approximation, arXiv preprint, arXiv:2012.14501.
 (A. Cohen, G. Petrova, and P. Wojtaszczyk), Optimal Stable Nonlinear Approximation, arXiv preprint, arXiv:2009.09907.
 (A. Cohen and W. Dahmen), State EstimationThe Role of Reduced Models, arXiv preprint, arXiv:2002.00220.
 (with A. Bonito, A. Cohen, D. Guignard, P. Jantsch and G. Petrova), Nonlinear Methods for Model Reduction, arXiv preprint, arXiv:2005.02565.
2019
 (with A. Bonito, D. Guignard, P. Jantsch and G. Petrova), Polynomial Approximation of Anisotropic Analytic Functions of Several Variables, (preprint), Constructive Approximation, (2020), 130.
 (with I. Daubechies, S. Foucart, B. Hanin and G. Petrova), Nonlinear Approximation and (Deep) ReLU Networks, arXiv preprint arXiv:1905.02199.
 (with A. Cohen, W. Dahmen, J. Fadili, O. Mula and J. Nichols), Optimal reduced model algorithms for databased state estimation, (preprint), SIAM Journal on Numerical Analysis, 58 (6), 33553381.
2018
 (with A. Cohen and W. Dahmen), Adaptive Wavelet Techniques in Numerical Simulation, Encyclopedia of Computational Mechanics Second Edition, (2018), 141.
 (with A. Cohen, W. Dahmen and J. Nichols), Reduced Basis Greedy Selection Using Random Training Sets, (preprint), M2AN Math. Model. Numer. Anal., 54 (2020), 15091524.
2017

(with S. Foucart, G. Petrova, and P. Wojtaszczyk), Computing a quantity of interest from observational data, (preprint) Constructive Approximation, 49 (3) (2019), 461508.

(with G. Petrova and P. Wojtaszczyk), Data assimilation and sampling in Banach spaces (preprint, arXiv:1602.06342), Calcolo, 54(2017), 9631007.
2016

(with A. Bonito, A. Cohen, G. Petrova, and G. Welper), Diffusion Coefficients Estimation for Elliptic Partial Differential Equations, (preprint), SIAM J. Math. Anal., 49(2)(2017), 15701592.

(with M. Bachmayr, A. Cohen, and G. Migliorati), Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients (preprint), arXic:1509.07050, M2AN, 51(1)(2015), 341363.

R. A. DeVore, The Theoretical Foundation of Reduced Basis Methods, Model Reduction and Approximation: Theory and Algorithms. (P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, Eds.), SIAM, Philadelphia, PA, (2017), 137168.
2015

(with P. Binev, A. Cohen, W. Dahmen, G. Petrova, and P. Wojtaszczyk), Data Assimilation in Reduced Modeling (preprint), SIAM UQ, 5(2017), 129.

(with A. Cohen and W. Dahmen), Orthogonal Matching Pursuit under the Restricted Isometry Property, Constructive Approximation, 45(1) (2017), 113127.

(with A. Cohen), Approximation of highdimensional parametric PDEs, Acta Numerica, (24)(2015), 1159.
2014

(with W. Dahmen, L. Grasedyck, and E. Süli), TensorSparsity of Solution to HighDimensional Elliptic Partial Differential Equations (preprint), Foundations of Computational Mathematics, 16(4)(2016), 813874.

(with A. Cohen) Kolmogorov widths under holomorphic mappings (preprint), IMA J. Numer. Anal., 36(1)(2016), 112.

(with V. Temlyakov), Convex optimization on Banach Spaces (preprint), Foundations of Computational Mathematics, 16(2)(2016), 369394.
2013

(with E. Zuazua), Recovery of initial temperature from discrete sampling, M3AS, 24(12)(2014), 24872501.

(with M. Bachmayr, W. Dahmen, and L. Grasedyck), Approximation of HighDimensional Rank One Tensors, Constructive Approximation, 39 (2014), 385395.

(with A. Cohen, G. Petrova, and P. Wojtaszczyk), Finding the minimum of a function, Methods and Applications of Analysis, 20(4)(2013), 365382.
2012

(with A. Bonito and R. Nochetto), Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients, SIAM J. Numer. Anal. 516 (2013), 31063134.

(with A. Cohen and R. Nochetto) Convergence Rates of AFEM with H^{1} Data, JofCM 12 (2012), 671718.

(with P. Binev, A. Cohen and W. Dahmen) Classification Algorithms using Adaptive Partitioning, Annals of Statisitics, 42(6)(2014), 21412163.

(with G. Petrova and P. Wojtaszczyk) Greedy Algorithms for Reduced Bases in Banach Spaces, Constructive Approximation, 37 (2013), 455466.
2011

(with G. Petrova, M. Hielsberg, L. Owens, B. Clack, and A. Sood) Processing Terrain Point Cloud Data, SIAM J. Imaging Sci,. 6(1)(2013), 131.

(with A. Chkifa, A. Cohen, and C. Schwab), Sparse Adaptive Taylor Approximation Algorithms for Parametric and Stochastic Elliptic PDEs, M2AN Math. Model. Numer. Anal., 47 (2013), 253280.
 (with A. Belochitski, P. Binev, M. FoxRabinovitz, V. Krasnopolski, and P. Lamby) Tree Approximation of the Long Wave Radiation Parameterization in the NCAR CAM Global Climate Model, Journal of Computational and Applied Mathematics, 236 (2011) 447460.
 (with G. Petrova and P. Wojtaszczyk), Approximating Functions of Few Variables in High Dimensions, Constructive Approximation, 33 (2011), 125143.

(with P. Binev, W. Dahmen, P. Lamby, D. Savu, R. Sharpley) Compressed Sensing and Electron Microscopy, Modeling Nanoscale Imaging in Electron Microscopy, Springer, (2011), 73126.

(with A. Cohen and C. Schwab), Analytic Regularity and Polynomial Approximation of Parametric Stochastic Elliptic PDEs, Analysis and Applications, 9 (2011), 1147.
 (with A. Cohen, I. Daubechies, G. Kerkyacharian, and D. Picard), Capturing Ridge Functions in High Dimensions from Point Queries, Constructive Approximation, 35 (2012), 225243.
 (with P. Binev, A. Cohen, W. Dahmen, G. Petrova, and P. Wojtaszczyk), Convergence Rates for Greedy Algorithms in Reduced Basis Methods (preprint), SIAM J. Math. Anal., 43 (2011), 14571472.
2010

(with A. Cohen and W. Dahmen), Instance Optimal Decoding by Thresholding in Compressed Sensing, in:Harmonic Analysis and Partial Differential Equations, Contemporary Mathematics 505 (2010), 127.

(with A. Ron), Approximation using Scattered Shifts of a Multivariate Function, TAMS, 362 (2010), 62056229.

(with A. Cohen, and C. Schwab), Convergence Rates of Best Nterm Galerkin Approximations for a Class of Elliptic sPDEs, Foundations of Computational Mathematics, 10 (2010), 615646.
 (with I. Daubechies, M. Fornasier and S. Gunturk), Iteratively reweighted least squares minimization for sparse recovery, Communications on Pure and Applied Mathematics, 63 No. 1, (2010), 138.
20092008
 (with I. Daubechies, M. Fornasier and S. Gunturk), Iteratively Reweighted Least Squares minimization: Proof of faster than linear rate for sparse recovery, Information Sciences and Systems, (2008), 2629.
 (with R. Baraniuk, M. Davenport, and M. Waken), A simple proof of the restricted isometry property for random matrices, Constructive Approximation, 28 (2008), 253263.
 (with A. Barron A. Cohen, and W. Dahmen), Approximation and Learning by Greedy Algorithms, Annals of Statistics, 36 (2008) 6494.
2007
 (with P. Bechler, A. Kamont, G. Petrova, and P. Wojtaszczyk), Greedy Wavelet Projections are Bounded on BV,
Trans. Amer. Math. Soc., 359 (2007) 637648.
 (with P. Binev, A. Cohen, and W. Dahmen), Universal Algorithms for Learning Theory Part II: Piecewise Polynomials,
Constructive Approximation, 26, No. 2 (2007) 127152.
 (with P. Binev, A. Cohen, and W. Dahmen), Universal Piecewise Polynomial Estimators for Machine Learning, in Curves and Surface Design,
Proceedings of the Avignon Conference (2006), (A. Cohen, J.L. Merrien, L. Shumaker, Eds.), Nashboro Press, 2007,4878.
 R. A. DeVore, Deterministic constructions of compressed sensing matrices, Journal of Complexity, 23 (2007) 918925.
 (with A. Cohen and W. Dahmen), A taste of compressed sensing, Proceedings of the SPIE Conference, Orlando, March 2007.
2006
 (with I. Daubechies, C. S. Gunturk, and V. Vaishampayan), A/D Conversion with an Imperfect Quantizer,
IEEE Trans. Inf. Theory, 52 (2006) 874885.
 (with G. Kerkyacharian, D. Picard and V. Temlyakov), On Mathematical Methods for Supervised Learning, J. of FOCM, 6 (2006) 358.
 (with P. Binev, A. Cohen, and W. Dahmen), Universal Piecewise Polynomial Estimators for Machine Learning, in Curves and Surface Design,
Proceedings of the Avignon Conference (2006), (A. Cohen, J.L. Merrien, L. Shumaker, Eds.), Nashboro Press, 2007, 4878.
2005
 (with A. Cohen, W. Dahmen, and M. CamposPinto), On the stability of nonlinear conservation laws in the Hausdorff metric,
J. Hyperbolic Differential Equations, 2 (2005) 2538.
 (with P. Binev, A. Cohen, W. Dahmen, and V. Temlyakov), Universal Algorithms for Learning Theory Part I: Piecewise Constant Functions,
J. Machine Learning, 6 (2005) 12971321.
 (with H. Narfi Stefansson, Kevin W. Eliceiri, Charles F. Thomas, Amos Ron, Robert Sharpley, and John G. White),
Wavelet Compression of ThreeDimensional TimeLapse Biological Image Data, Microsc. Microanal., 11 (2005) 917.
2004
 (with Peter Binev), Fast Computation in Adaptive Tree Approximation, Numerische Mathematik, 97 (2004) 193217.
 (with Peter Binev and W. Dahmen), Adaptive Finite Element Methods with Convergence Rates, Numerische Mathematik, 97 (2004) 219268.
 (with P. Binev, W. Dahmen, and N. Dyn), Adaptive Approximation of Curves, Approximation Theory: A volume dedicated to Borislav Bojanov
(D.K. Dimitrov, G. Nikolov, and R. Uluchev, Eds.), Marin Drinov Academic Publishing House, Sofia (2004), 4357.
 (with A. Kurdila, M. Nechyba, R. Lind, P. Ifju, P. Binev, W. Dahmen, and R. Sharpley), VisionBased Control of MicroAirVehicles:
Progress and Problems in Estimation, 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, December 2004,
16361642. Appeared IEEE Decision and Control.
2003
 (with A. Cohen, W. Dahmen, and I. Daubechies), Harmonic Analysis of the Space BV, Revista Matematica Iberoamericana, 19 (2003) 235263.
 (with I. Daubechies), Reconstructing a bandlimited function from very coarsely quantized data: A family of stable sigmadelta modulators
of arbitrary order, Annals of Mathematics, 158 (2003) 643674.
 (with A. Cohen and W. Dahmen), Sparse Evaluation of Compositions of Functions Using Multiscale Expansions,
SIAM J. Math. Anal., 35 (2003) 279303.
 (with G. Petrova and V. Temlyakov), Best Basis Selection for Approximation in L_{p} , J. of FoCM, 3 (2003) 161185.
 (with A. Cohen and W. Dahmen), Adaptive Wavelet Schemes for Nonlinear Variational Problems,
SIAM J. Numer. Anal., 41, No. 5 (2003) 17851823.
2002
 (with R. Baraniuk, G. Kyriazis, and X.M. Yu), Near Best tree approximation, Advances in Comp. Math, 16 (2002) 357373.
 (with A. Cohen, W. Dahmen), Adaptive Wavelet Methods II: beyond the elliptic case, J. FoCM, 2, no. 3 (2002) 203245.
 (with I. Daubechies, C. S. Gunturk, and V. Vaishampayan), Beta Expansions: A New Approach to Digitally Corrected A/D Conversion,
Proceedings of the IEEE Intl. Symposium of Circuits and Systems, Scottsdale, Arizona, May 2002, 2629.
 (with A. Petukhov and R. C. Sharpley), Motion Estimation with the Redundant Wavelet Transform,
The Third International Workshop on Digital and Computational Video, M.A. Bayoumi (ed.), IEEE Proceedings, St. Petersburg, Fl., 2002, 5359.
 (with Peter Binev, W. Dahmen, and P. Petrushev), Approximation Classes for Adaptive Methods, Serdica Math. J., 28 (2002) 391416.
2001
 (with A. Cohen, W. Dahmen, and I. Daubechies), Tree Approximation and Encoding, ACHA, 11 (2001) 192226.
 (with A. Cohen, G. Kerkyacharian, and D. Picard), Maximal Spaces with given rate of convergence for thresholding algorithms,
ACHA, 11 (2001) 167191.
2000
 (with A. Cohen and W. Dahmen), Multiscale decompositions on bounded domains, Transactions AMS, 352 (2000) 36513685.
 (with A. Cohen and R. Hochmuth), Restricted nonlinear approximation, Constructive Approximation, 16 (2000) 85113.
 (with H. Wang, J. Liu and H. Xu), A CFLfree explicit scheme with compression for linear hyperbolic equations,
Lecture Notes in Physics, 552 (2000) 116123.
 (with A. Cohen, W. Dahmen), Adaptive wavelet methods for elliptic operator equations: convergence rates, Math. Comp., 70 (2000) 2775.
 (with G. Petrova), The Averaging Lemma, J. Am. Math. Soc., 14 (2000) 279296.
 (with L.S. Johnson, C. Pan, and R. Sharpley), Optimal entropy encoders for mining multiply resolved data,
Data Mining II (N. Ebecken and C.A. Brebbia, Eds.), WIT Press, Boston, 2000, 7382.