Zobrazeno 1 - 10
of 251
pro vyhledávání: '"DeVore, Ronald A."'
We determine the best n-term approximation of generalized Wiener model classes in a Hilbert space $H $. This theory is then applied to several special cases.
Externí odkaz:
http://arxiv.org/abs/2406.10761
We provide an a priori analysis of a certain class of numerical methods, commonly referred to as collocation methods, for solving elliptic boundary value problems. They begin with information in the form of point values of the right side f of such eq
Externí odkaz:
http://arxiv.org/abs/2406.09217
We construct uniformly bounded solutions of the equation $div\, {\mathbf u}=f$ for arbitrary data $f$ in the critical spaces $L^d(\Omega)$, where $\Omega$ is a domain of ${\mathbb R}^d$. This question was addressed by Bourgain & Brezis, [On the equat
Externí odkaz:
http://arxiv.org/abs/2405.12703
Publikováno v:
Applied and Computational Harmonic Analysis, vol. 74, no. 101713, pp. 1-22, 2025
We investigate the approximation of functions $f$ on a bounded domain $\Omega\subset \mathbb{R}^d$ by the outputs of single-hidden-layer ReLU neural networks of width $n$. This form of nonlinear $n$-term dictionary approximation has been intensely st
Externí odkaz:
http://arxiv.org/abs/2307.15772
Autor:
Binev, Peter, Bonito, Andrea, Cohen, Albert, Dahmen, Wolfgang, DeVore, Ronald, Petrova, Guergana
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when the bounda
Externí odkaz:
http://arxiv.org/abs/2301.05540
Publikováno v:
In Applied and Computational Harmonic Analysis January 2025 74
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings for this le
Externí odkaz:
http://arxiv.org/abs/2203.15994
Autor:
Daubechies, Ingrid, DeVore, Ronald, Dym, Nadav, Faigenbaum-Golovin, Shira, Kovalsky, Shahar Z., Lin, Kung-Ching, Park, Josiah, Petrova, Guergana, Sober, Barak
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there exists a variet
Externí odkaz:
http://arxiv.org/abs/2107.13191
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical explanation for
Externí odkaz:
http://arxiv.org/abs/2012.14501
While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies nonlinear meth
Externí odkaz:
http://arxiv.org/abs/2009.09907