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math.NA2026
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…
math.NA2026
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…
math.NA2025
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…