102 citations · 116 across the 18 of their papers we have counts for
23 papers
Constrained Kolmogorov widths
Ronald DeVore, Guergana Petrova, Jonathan W. Siegel +1
The main theme of approximation theory is to understand how well a general function can be approximated by a simpler function such as a polynomial or spline. In many applic…
Sampling and reconstruction of convex functions
Andrea Bonito, Albert Cohen, Wolfgang Dahmen +3
We discuss optimal recovery for classes of multivariate convex functions from given point samples, as well as the sampling numbers of these classes, corresponding to optimal sample…
Optimal Recovery Meets Minimax Estimation
Ronald DeVore, Robert D. Nowak, Rahul Parhi +2
A fundamental problem in statistics and machine learning is to estimate a function from possibly noisy observations of its point samples. The goal is to design a numerical algo…
A note on best n-term approximation for generalized Wiener classes
Ronald DeVore, Guergana Petrova, Przemyslaw Wojtaszczyk
We determine the best n-term approximation of generalized Wiener model classes in a Hilbert space . This theory is then applied to several special cases.
Convergence and error control of consistent PINNs for elliptic PDEs
Andrea Bonito, Ronald DeVore, Guergana Petrova +1
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize…
Solving PDEs with Incomplete Information
Peter Binev, Andrea Bonito, Albert Cohen +3
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. O…