philipp grohs
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Optimal approximation with sparsely connected deep neural networks
H Bolcskei, P Grohs, G Kutyniok, P Petersen
SIAM Journal on Mathematics of Data Science 1 (1), 8-45, 2019
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
P Grohs, F Hornung, A Jentzen, P Von Wurstemberger
Memoirs of the American Mathematical Society, 2018
Parabolic molecules
P Grohs, G Kutyniok
Foundations of Computational Mathematics 14 (2), 299-337, 2014
Laguerre minimal surfaces, isotropic geometry and linear elasticity
H Pottmann, P Grohs, NJ Mitra
Advances in computational mathematics 31 (4), 391, 2009
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of …
J Berner, P Grohs, A Jentzen
SIAM Journal on Mathematics of Data Science 2 (3), 631-657, 2020
Solving stochastic differential equations and Kolmogorov equations by means of deep learning
C Beck, S Becker, P Grohs, N Jaafari, A Jentzen
arXiv preprint arXiv:1806.00421, 2018
Deep neural network approximation theory
D Elbrächter, D Perekrestenko, P Grohs, H Bölcskei
IEEE Transactions on Information Theory, 2019
Continuous shearlet frames and resolution of the wavefront set
P Grohs
Monatshefte für Mathematik 164 (4), 393-426, 2011
Smoothness properties of Lie group subdivision schemes
J Wallner, EN Yazdani, P Grohs
Multiscale modeling & simulation 6 (2), 493-505, 2007
DNN expression rate analysis of high-dimensional PDEs: Application to option pricing
D Elbrächter, P Grohs, A Jentzen, C Schwab
arXiv preprint arXiv:1809.07669, 2018
ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds
P Grohs, S Hosseini
Advances in Computational Mathematics 42 (2), 333-360, 2016
A general proximity analysis of nonlinear subdivision schemes
P Grohs
SIAM Journal on Mathematical Analysis 42 (2), 729-750, 2010
Stable phase retrieval in infinite dimensions
R Alaifari, I Daubechies, P Grohs, R Yin
Foundations of Computational Mathematics 19 (4), 869-900, 2019
Optimal a priori discretization error bounds for geodesic finite elements
P Grohs, H Hardering, O Sander
Foundations of Computational Mathematics 15 (6), 1357-1411, 2015
Interpolatory wavelets for manifold-valued data
P Grohs, J Wallner
Applied and Computational Harmonic Analysis 27 (3), 325-333, 2009
Smoothness analysis of subdivision schemes on regular grids by proximity
P Grohs
SIAM journal on numerical analysis 46 (4), 2169-2182, 2008
Phase retrieval in the general setting of continuous frames for Banach spaces
R Alaifari, P Grohs
SIAM journal on mathematical analysis 49 (3), 1895-1911, 2017
P Grohs, S Keiper, G Kutyniok, M Schäfer
Applied and Computational Harmonic Analysis 41 (1), 297-336, 2016
Smoothness equivalence properties of univariate subdivision schemes and their projection analogues
P Grohs
Numerische Mathematik 113 (2), 163-180, 2009
Continuous shearlet tight frames
P Grohs
Journal of Fourier Analysis and Applications 17 (3), 506-518, 2011
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