1. Discretization Theorems for Entire Functions of Exponential Type
   2025/05/21 by Michael I. Ganzburg, Ganzburg, Michael I. · 1 citation
   Mathematics · #26D15 #41A63 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 26D07 #Secondary 41A10
2. Kernel interpolation on generalized sparse grids
   2025/05/18 by Griebel, Michael, Harbrecht, Helmut, Multerer, Michael · 1 citation
   #41A46 #41A63 #46E35 #FOS: Mathematics #Numerical Analysis (math.NA)
3. Surrogate to Poincaré inequalities on manifolds for dimension reduction in nonlinear feature spaces
   2025/05/03 by Nouy, Anthony, Pasco, Alexandre · 1 citation
   #41A10 #41A63 #60F10 #65D15 #65D40 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
4. Bi-Lipschitz Ansatz for Anti-Symmetric Functions
   2025/03/06 by Dym, Nadav, Lu, Jianfeng, Mizrachi, Matan · 2 citations
   #41A29 #41A63 #68T07 #81Q05 #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #G.1.10 #G.1.2 #I.5.1 #I.5.4 #Machine Learning (cs.LG) #Quantum Physics (quant-ph)
5. Constructive Approximation of High-Dimensional Functions with Small Efficient Dimension with Applications in Uncertainty Quantification
   2024/11/27 by Christian Rieger, Rieger, Christian, Holger Wendland +1 · 1 citation
   Decision Sciences · #41A25 #41A63 #65D05 #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
6. Quasi-interpolation for high-dimensional function approximation
   2024/09/22 by Gao, Wenwu, Wang, Jiecheng, Sun, Zhengjie +1 · 2 citations
   #41A05 #41A25 #41A30 #41A63 #42B05 #65D15 #65D40 #FOS: Mathematics #Numerical Analysis (math.NA)
7. Addressing common misinterpretations of KART and UAT in neural network literature
   2024/08/29 by Ismailov, Vugar · 1 citation
   #26B40 #41A30 #41A63 #68T05 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Neural and Evolutionary Computing (cs.NE)
8. Weighted least ℓ_p approximation on compact Riemannian manifolds
   2024/02/29 by Li, Jiansong, Ling, Yun, Geng, Jiaxin +1 · 1 citation
   #41A17 #41A55 #41A63 #65D15 #65D30 #65D32 #FOS: Mathematics #Numerical Analysis (math.NA)
9. Sharp Bernstein inequalities on simplex
   2023/07/04 by Ge, Yan, Xu, Yuan · 1 citation
   #41A10 #41A63 #42C10 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
10. Sampling recovery in L₂ and other norms
    2023/05/12 by Krieg, David, Pozharska, Kateryna, Ullrich, Mario +1 · 2 citations
    #41A50 #41A63 #46B09 #47B06 #68Q25 #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)
11. On the universal approximation property of radial basis function neural networks
    2023/04/05 by Ismayilova, Aysu, Ismayilov, Muhammad · 1 citation
    #41A30 #41A63 #68T05 #92B20 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
12. Optimal approximation using complex-valued neural networks
    2023/03/29 by Paul Geuchen, Felix Voigtlaender, Geuchen, Paul +1 · 1 citation
    Computer Science · Materials Science · #30E10 #31A30 #41A30 #41A63 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine Learning in Materials Science #Neural Networks and Applications
13. A comparison of rational and neural network based approximations
    2023/03/08 by Vinesha Peiris, Peiris, Vinesha, R. Díaz Millán +5 · 1 citation
    Computer Science · Engineering · #41A20 #41A50 #41A63 #65D10 #65D12 #65D15 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Reservoir Engineering and Simulation Methods
14. Compositional Sparsity, Approximation Classes, and Parametric Transport Equations
    2022/07/13 by Dahmen, Wolfgang · 4 citations
    #35A35 #35B30 #35L04 #41A25 #41A46 #41A63 #FOS: Mathematics #Numerical Analysis (math.NA)
15. On Fekete Points for a Real Simplex
    2022/05/13 by Len Bos, Bos, Len · 1 citation
    Mathematics · #41A17 #41A63 #Analytic and geometric function theory #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA)
16. Constructive subsampling of finite frames with applications in optimal function recovery
    2022/02/25 by Bartel, Felix, Schäfer, Martin, Ullrich, Tino · 2 citations
    #41A10 #41A25 #41A60 #41A63 #42A10 #68Q25 #68W40 #94A20 #FOS: Mathematics #Numerical Analysis (math.NA)
17. A Spline Dimensional Decomposition for Uncertainty Quantification in High Dimensions
    2021/11/25 by Sharif Rahman, Ramin Jahanbin, Rahman, Sharif +1 · 1 citation
    Decision Sciences · Engineering · #26B99 #41A10 #41A63 #46N30 #60H10 #60H25 #60H30 #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Scientific Measurement and Uncertainty Evaluation #Statistics Theory (math.ST) #Structural Health Monitoring Techniques
18. Sparse grid approximation in weighted Wiener spaces
    2021/11/11 by Kolomoitsev, Yurii, Lomako, Tetiana, Tikhonov, Segey · 1 citation
    #41A17 #41A25 #41A58 #41A63 #42A10 #42A15 #42B25 #42B35 #FOS: Mathematics #Numerical Analysis (math.NA)
19. Sampling discretization of integral norms and its application
    2021/09/18 by Dai, F., Temlyakov, V. · 1 citation
    #41A63 #65D30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Primary 65J05 #Secondary 42A05
20. Approximation and localized polynomial frame on conic domains
    2020/11/28 by Xu, Yuan · 3 citations
    #41A10 #41A63 #42C10 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
21. Random points are optimal for the approximation of Sobolev functions
    2020/09/23 by Krieg, David, Sonnleitner, Mathias · 2 citations
    #41A25 #41A63 #62D05 #65D15 #65D30 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)
22. Multivariate Rational Approximation Using a Stabilized\n Sanathanan-Koerner Iteration
    2020/09/22 by Jeffrey M. Hokanson, Hokanson, Jeffrey M. · 2 citations
    Computer Science · Decision Sciences · Engineering · Physics and Astronomy · #41A20 #41A63 #65D15 #Control Systems and Identification #FOS: Mathematics #Lightning and Electromagnetic Phenomena #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Probabilistic and Robust Engineering Design
23. A deep network construction that adapts to intrinsic dimensionality\n beyond the domain
    2020/08/06 by Alexander Cloninger, Timo Klock, Cloninger, Alexander +1 · 1 citation
    Computer Science · Physics and Astronomy · #41A25 #41A46 #41A63 #62G05 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques
24. Universal approximation of symmetric and anti-symmetric functions
    2019/12/04 by Jiequn Han, Han, Jiequn, Yingzhou Li +9 · 1 citation
    Mathematics · #41A25 #41A29 #41A63 #Approximation Theory and Sequence Spaces #Chemical Physics (physics.chem-ph) #FOS: Mathematics #FOS: Physical sciences #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)
25. Worst-case recovery guarantees for least squares approximation using\n random samples
    2019/11/22 by Lutz Kämmerer, Tino Ullrich, Kämmerer, Lutz +3 · 2 citations
    Mathematics · Medicine · #41A10 #41A25 #41A55 #41A60 #41A63 #42A10 #65D32 #65Txx #68Q25 #68W40 #94A20 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA) #Statistical and numerical algorithms
26. Universal Approximation with Deep Narrow Networks
    2019/05/21 by Kidger, Patrick, Lyons, Terry · 12 citations
    #41A46 #41A63 #68T07 #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML)
27. A Polynomial Chaos Expansion in Dependent Random Variables
    2018/04/12 by Rahman, Sharif · 1 citation
    #26B99 #41A10 #41A63 #46N30 #60H10 #60H25 #60H30 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Statistics Theory (math.ST)
28. Mathematical Properties of Polynomial Dimensional Decomposition
    2018/04/05 by Rahman, Sharif · 1 citation
    #26B99 #41A63 #41A99 #65C60 #65G99 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Statistics Theory (math.ST)
29. Gradient-based dimension reduction of multivariate vector-valued functions
    2018/01/24 by Zahm, Olivier, Constantine, Paul, Prieur, Clémentine +1 · 1 citation
    #41A30 #41A63 #65D15 #Analysis of PDEs (math.AP) #FOS: Mathematics
30. H²--Convergence of least-squares kernel collocation methods
    2018/01/02 by Cheung, Ka-Chun, Ling, Leevan, Schaback, Robert · 1 citation
    #41A63 #65D15 #65N35 #FOS: Mathematics #Numerical Analysis (math.NA)

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