Refereed Publications:

• P. Binev, A. Bonito, R. DeVore, G. Petrova, Optimal Learning, submitted

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• I. Daubechies, R. DeVore, N. Dym, S. Faugenbaum-Golovin, S. Kovalsky, K-C. Lin, J. Park, G. Petrova, B. Sober, Neural Network Approximation of Ferinable Functions, IEEE Transactions of Information Theory, submitted.

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• G. Petrova, P. Wojtaszczyk, On the Entropy Numbers and the Kolmogorov Widths, Pure and Applied Functional Analysis, to appear.

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• G. Petrova, P. Wojtaszczyk, Lipschitz Widths, Constructive Approximation, to appear.

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• A. Cohen, R. DeVore, G. Petrova, P. Wojtaszczyk, Optimal Stable Nonlinear Approximation, J. FOCM, to appear

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• R. DeVore, B. Hanin, G. Petrova, Neural Network Approximation, Acta Numerica, 30 (2021), 327-444.

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• A. Bonito, A. Cohen, R. DeVore, D. Guignard, P. Jantsch, G. Petrova,
  Nonlinear Methods for Model Reduction, M2AN Math. Model. Numer. Anal. 55(2) (2021), 507-531.

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• I. Daubechies, R. DeVore, S. Foucart, B. Hanin, and G. Petrova,
  Nonlinear Approximation and (Deep) ReLU Networks, Constructive Approximation, 55(1) (2022), 127-172.

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• A. Bonito, R. DeVore, D. Guignard, P. Jantsch, and G. Petrova
  Polynomial Approximation of Anisotropic Analytic Functions of Several Variables, Constructive Approximation, 53(2) (2021), 319-348.

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• Z. Gao, G. Petrova,
  Rescaled Pure Greedy Algorithm  for Convex Optimization, Calcolo, 56(2) (2019), article 15

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• S. Foucart, M. Hielsberg, G. Mullendore, G. Petrova, P. Wojtaszczyk,
  Optimal algorithms for computing average temperatures, Math. Clim. Weather Forecast., 5 (2019), 34--44.

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• R. DeVore, S. Foucart, G. Petrova, and P. Wojtaszczyk,
  Computing a Quantity of Interest from Observational Data, Constr. Approx., 49(3) (2019), 461-508.

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• R. DeVore, G. Petrova, and P. Wojtaszczyk,
  Data Assimilation and Sampling in Banach spaces, Calcolo, 54(3) (2017), 963--1007.

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• A. Bonito, A. Cohen, R. DeVore, G. Petrova, and G. Welper,
  Diffusion Coefficients Estimation for Elliptic Equations, SIAM J. Math. Anal., 49(2) (2017), 1570–-1592.

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• P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk,
  Data Assimilation in Reduced Modeling, SIAM J. on Uncertainty Quantification, 5(1) (2017), 1--29.

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• G. Petrova,
  Generalized Gauss-Radau and Gauss-Lobatto formulas with Jacobi weight functions, BIT Numerical Mathematics, 57(1) (2017), 191--206.

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• H. Nguyen, G. Petrova,
  Greedy Strategies for Convex Optimization, Calcolo, 54(1) (2017), 207--224.

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• G. Petrova,
  Rescaled Pure Greedy Algorithm for Hilbert and Banach Spaces, Appl. Comput. Harm. Analysis, 41 (2016), 852--866.

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• H. Nguyen, G. Petrova,
  Extended Gaussian Type Cubatures for the Ball, J. Comp. Applied Math., 290 (2015), 209--223.

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• D. Jimenez, G. Petrova,
  On Matching Point Configurations, Constructive Theory of Functions, 141-154, 2014.

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• A. Cohen, R. DeVore, G. Petrova, P. Wojtaszczyk,
  Finding the Minimum of a Function, Methods and Applications of Analysis, (20)4 (2013), 393--410.

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• R. DeVore, G. Petrova, P. Wojtaszczyk,
  Greedy Algorithms for Reduced Bases in Banach Spaces, Constr. Approx., (37)3 (2013), 455--466.

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• R. DeVore, G. Petrova, M. Hielsberg, L. Owens, B. Clack, A. Sood,
  Processing Terrain Point Cloud Data, SIAM J. Imaging Sci., 6(1) (2013), 1--31.

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• J. Smith, G. Petrova, S. Schaefer,
  Progressive Encoding and Compression of Surfaces Generated from Point Cloud Data, Computers&Graphics (Proceedings of Shape Modeling International 2012), 36(5) (2012), 341--348.

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• J. Smith, G. Petrova, S. Schaefer,
  Encoding Normal Vectors Using Optimized Spherical Coordinates, Computers&Graphics (Proceedings of Shape Modeling International 2012), 36(5) (2012), 360--365.

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• P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, P. Wojtaszczyk,
  Convergence Rates for Greedy Algorithms in Reduced Basis Methods, SIAM J. Math. Anal., 43(3) (2011), 1457--1472.

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• R. DeVore, G. Petrova, P. Wojtaszczyk,
  Approximation of Functions of Few Variables in High Dimensions, Constr. Approx., 33(1) (2011), 125--143.

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• S. Bryson, Y. Epshteyn, A. Kurganov, G. Petrova,
  Well-balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System, M2AN Math. Model. Numer. Anal., 45(3) (2011), 423--446.

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• B. Bojanov, G. Petrova,
  Quadrature Formula for Computed Tomography, J. Approx. Theory, 162(10) (2010), 1788--1792.

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• B. Bojanov, G. Petrova,
  Quadrature formulas for Fourier coefficients, J. Comp. Applied Math., 231 (2009), 378--391.

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• A. Kurganov, G. Petrova,
  Central-upwind schemes for two-layer shallow water equations,SIAM J. SCi. Comput., 31(3) (2009), 1742--1773.

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• R. DeVore, G. Petrova, P. Wojtaszczyk,
  Instance-optimality in Probability with an l_1-Minimization Decoder, Appl. Comput. Harm. Analysis, 27(3) (2009), 275--288.

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• A. Chertock, A. Kurganov, G. Petrova,
  Fast Explicit Operator Splitting Method for Convection-Diffusion Equations, Int. J. Numer. Meth. Fluids, 59 (2009), no. 3, 309--332.

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• J. Manson, G. Petrova, S. Schaefer,
  Streaming surface reconstruction using wavelets, Computer Graphics Forum (Proceedings of the Symposium on Geometry Processing), 27 (2008), no. 5, 1411--1420.

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• R. DeVore, G. Petrova and P. Wojtaszczyk,
  Anisotropic smoothness spaces via level sets, Commun. Pur Appl. Math., 61 (2008), no. 9, 1264--1297.

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• A. Kurganov, G. Petrova,
  A Central-upwind scheme for landslides-generated water waves, Hyperbolic Problems: Theory, Numerics, Applications (Lyon, 2006), 635--642, Springer, 2008.

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• A. Kurganov, G. Petrova and B. Popov,
  Adaptive semi-discrete central-upwind schemes for nonconvex hyperbolic conservation laws, SIAM J. Sci. Comput., 29(6) (2007), 2381--2401.

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• A. Kurganov, G. Petrova,
  A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system, Comm. Math. Sci., 5(1) (2007), 133--160.

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• P. Bechler, R. DeVore, A. Kamont, G. Petrova, P. Wojtaszczyk,
  Greedy wavelet projections are bounded on BV, Trans. Amer. Math. Soc., 359 (2007), 637--648.

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• A. Kurganov, G. Petrova,
  Adaptive Central-Upwind Schemes for Hamilton-Jacobi Equations with Nonconvex Hamiltonians, J. Sci. Comput., 27 (2006), 323--333.

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• A. Chertock, A. Kurganov and G. Petrova,
  Finite-Volume-Particle Methods for Models of Transport of Pollutant in Shallow Water, J. Sci. Comput., 27 (2006), 189--199.

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• A. Chertock, A. Kurganov and G. Petrova
  Fast Explicit Operator Splitting Method. Application to the Polymer System, Proceedings of the Fourth International Symposium on Finite Volumes for Complex Applications, Marrakech, 63--72,2005.

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• A. Kurganov, G. Petrova
  Central-Upwind Schemes on Triangular Grids for Hyperbolic Systems of Conservation Laws, Numer. Methods Partial Differential Equations, 21(3) (2005), 536--552.

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• S. Bryson, A. Kurganov, D. Levy and G. Petrova
  Semi-Discrete Central-Upwind Schemes with Reduced Dissipation for Hamilton-Jacobi Equations, IMA J. Numer. Anal., 25 (2005), 113--138.

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• D. Dimitrov, G. Petrova
  Extended cubature formula of Turan type (0,2) for the ball, Approximation theory, A volume dedicated to Borislav Bojanov, 64-72, 2004.

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• S. Karni, E. Kirr, A. Kurganov and G. Petrova
  Compressible Two-Phase Flows by Central and Upwind Schemes, M2AN Math. Model. Numer. Anal., 38 (2004), no. 3, 477--493.

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• J. Otero, L. Dontcheva, H. Johnston, R. Worthing, A. Kurganov, G. Petrova and C. Doering
  High Raleigh Number Convection in a Fluid Saturated Porous Layer, Journal of Fluid Mechanics, 500 (2004), 263--281.

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• G. Petrova
  Cubature formulae for spheres, simplices and balls, J. Comput. Appl. Math. 162(2) (2004), 483--496.

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• G. Petrova
  Uniqueness of the Gaussian extended cubature for polyharmonic functions, East J. Approx. 9 (2003), no. 3, 269--275.

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• R. DeVore, G. Petrova and V. Temlyakov
  Best basis selection for approximation in $L\sb p$, Found. Comput. Math. 3 (2003), no. 2, 161--185.

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• G. Petrova
  Cubature formulae for the sphere and the ball in $R^n$, Proceedings volume of ``Constructive Theory of Functions'', Varna 2002, (B. Bojanov, Ed.), DARBA, Sofia, 380-384, 2003.

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• S. Karni, A. Kurganov, G. Petrova
  A smoothness indicator for adaptive algorithms for hyperbolic systems, J. Comput. Phys. 178 (2002), no. 2, 323--341.

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• A. Kurganov, S. Noelle, G. Petrova
  Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23 (2001), no. 3, 707--740 (electronic).

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• G. Petrova, B. Popov
  Linear transport equations with mu-monotone coefficients, J. Math. Anal. Appl. 260 (2001), no. 2, 307--324.

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• A. Kurganov, G. Petrova
  A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math. 88 (2001), no. 4, 683--729.

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• R. DeVore, G. Petrova
  The averaging lemma, J. Amer. Math. Soc. 14 (2001), no. 2, 279--296 (electronic).

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• A. Kurganov, G. Petrova
  Central schemes and contact discontinuities, M2AN Math. Model. Numer. Anal. 34 (2000), no. 6, 1259--1275.

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• B. Bojanov, G. Petrova
  Uniqueness of the Gaussian quadrature for a ball, J. Approx. Theory 104 (2000), no. 1, 21--44.

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• G. Petrova, B. Popov
  Linear transport equations with discontinuous coefficients, Comm. Partial Differential Equations 24 (1999), no. 9-10, 1849--1873.

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• B. Bojanov, G. Petrova
  Numerical integration over a disc. A new Gaussian quadrature formula, Numer. Math. 80 (1998), no. 1, 39--59.

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• B. Bojanov, G. Petrova
  On minimal cubature formulae for product weight functions, J. Comput. Appl. Math. 85 (1997), no. 1, 113--121.

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