1. Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate
   2025/06/09 by Bartel, Felix, Gilbert, Alexander D., Kuo, Frances Y. +1 · 3 citations
   #41A25 #94A20 #FOS: Mathematics #Numerical Analysis (math.NA)
2. Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective
   2025/04/18 by Jiao, Yuling, Lai, Yanming, Wang, Yang +1 · 1 citation
   #41A25 #68T07 #68T50 #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #G.0 #Machine Learning (cs.LG)
3. 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
4. FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
   2024/11/16 by Arghya Sinha, Sinha, Arghya, Kunal N. Chaudhury +1 · 1 citation
   Computer Science · #41A25 #65F10 #94A08 #FOS: Electrical engineering #FOS: Mathematics #Image and Video Processing (eess.IV) #Neural Networks and Applications #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques #electronic engineering #information engineering
5. Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains
   2024/11/06 by Abdeljawad, Ahmed, Dittrich, Thomas · 3 citations
   #41A25 #41A30 #41A46 #46E35 #62M45 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
6. Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces
   2024/11/06 by Yurii Kolomoitsev, Kolomoitsev, Yurii, Sergey Tikhonov +1 · 1 citation
   Mathematics · #41A25 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)
7. Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression
   2024/10/08 by Ou, Weigutian, Bölcskei, Helmut · 1 citation
   #41A25 #62G08 #68T07 #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
8. 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)
9. Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
   2024/08/01 by Imbert-Gérard, Lise-Marie, Moiola, Andrea, Perinati, Chiara +1 · 2 citations
   #35J25 #41A10 #41A25 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)
10. Korovkin-type approximation for non-positive operators
    2024/03/06 by Kumar, V. B. Kiran, Namboodiri, M. N. N., Vinaya, P. C. · 1 citation
    #41A25 #41A35 #41A36 #46B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
11. Approximation of the Koopman operator via Bernstein polynomials
    2024/03/04 by Yadav, Rishikesh, Mauroy, Alexandre · 1 citation
    #37L65 #37M15 #41A25 #41A36 #47B33 #Dynamical Systems (math.DS) #FOS: Mathematics
12. Convergence analysis of Hermite approximations for analytic functions
    2023/12/13 by Haiyong Wang, Wang, Haiyong, Lun Zhang +1 · 1 citation
    Mathematics · #41A05 #41A10 #41A25 #65D30 #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Analysis (math.NA)
13. Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces
    2023/12/13 by Ahmed Abdeljawad, Abdeljawad, Ahmed, Thomas Dittrich +1 · 1 citation
    Physics and Astronomy · #41A25 #41A30 #41A46 #46E35 #62M45 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks
14. Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms
    2023/11/08 by Yang, Yahong, Lu, Yulong · 1 citation
    #41A25 #41A46 #65D07 #68Q25 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
15. Performance bounds for Reduced Order Models with Application to Parametric Transport
    2023/10/22 by Rim, D., Welper, G. · 1 citation
    #41A25 #41A46 #65N15 #FOS: Mathematics #Numerical Analysis (math.NA)
16. Spectral Barron space for deep neural network approximation
    2023/09/02 by Liao, Yulei, Ming, Pingbing · 5 citations
    #32C22 #32K05 #33C20 #41A25 #41A46 #42A38 #68T07 #FOS: Mathematics #Numerical Analysis (math.NA)
17. Polynomial Interpolation of Function Averages on Interval Segments
    2023/09/01 by Ludovico Bruni Bruno, Bruno, Ludovico Bruni, Wolfgang Erb +1 · 9 citations
    Computer Science · #41A05 #41A10 #41A25 #65D05 #Digital Filter Design and Implementation #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
18. Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks
    2023/07/28 by Siegel, Jonathan W. · 2 citations
    #41A25 #41A46 #52A21 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
19. Error estimate of the u-series method for molecular dynamics simulations
    2023/05/09 by Liang, Jiuyang, Xu, Zhenli, Zhou, Qi · 3 citations
    #41A25 #42A38 #68W40 #82M37 #FOS: Mathematics #Numerical Analysis (math.NA)
20. A source identification problem in a bi-parabolic equation: convergence rates and some optimal results
    2023/04/17 by Subhankar Mondal, Mondal, Subhankar, M. Thamban Nair +1 · 1 citation
    Computer Science · Engineering · Mathematics · #35R25 #41A25 #47A52 #65M30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
21. Rate of Convergence in Periodic Homogenization for Convex Hamilton-Jacobi Equations with Multiscales
    2023/03/10 by Yuxi Han, Han, Yuxi, Ji-Woong Jang +1 · 3 citations
    Computer Science · Mathematics · #35B27 #35F21 #41A25 #49L25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations
22. Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms
    2023/02/14 by Thomas Hangelbroek, Hangelbroek, Thomas, Christian Rieger +1 · 2 citations
    Engineering · #41A17 #41A25 #65D12 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
23. A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility
    2022/11/02 by Dianming Hou, Hou, Dianming, Lili Ju +3 · 4 citations
    Materials Science · Mathematics · #41A05 #41A25 #65M06 #65M15 #Differential Equations and Numerical Methods #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA) #Numerical methods for differential equations #Solidification and crystal growth phenomena
24. An improved bound on Legendre approximation
    2022/07/27 by Hamzehnejad, M., Hosseini, M. M., Salemi, A. · 1 citation
    #41A25 #FOS: Mathematics #Numerical Analysis (math.NA)
25. 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)
26. Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations
    2022/06/20 by Belomestny, Denis, Naumov, Alexey, Puchkin, Nikita +1 · 6 citations
    #41A15 #41A25 #41A28 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Statistics Theory (math.ST)
27. Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness
    2022/03/08 by Griebel, Michael, Harbrecht, Helmut, Schneider, Reinhold · 3 citations
    #41A17 #41A25 #41A30 #41A65 #FOS: Mathematics #Numerical Analysis (math.NA)
28. 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)
29. 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)
30. Optimal Convergence Rates for the Orthogonal Greedy Algorithm
    2021/06/28 by Siegel, Jonathan W., Xu, Jinchao · 1 citation
    #41A25 #41A46 #46N30 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST)

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