Jonathan W. Siegel

activity

20232026

collaborators

5 papers

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 $f$ can be approximated by a simpler function $g$ 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.FA2025

Nearly optimal bounds on the Fourier sampling numbers of Besov spaces

Jonathan W. Siegel

Let $T^{d}$ denote the $d$ -dimensional torus. We consider the problem of optimally recovering a target function $f^{*} : T^{d} \to C$ from samples of its…

math.NA2024

Sharp Lower Bounds on the Manifold Widths of Sobolev and Besov Spaces

Jonathan W. Siegel

We consider the problem of determining the manifold $n$ -widths of Sobolev and Besov spaces with error measured in the $L_{p}$ -norm. The manifold widths control how efficiently these…

math.OC2023

A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces

Jonathan W. Siegel, Stephan Wojtowytsch

We consider gradient flow/gradient descent and heavy ball/accelerated gradient descent optimization for convex objective functions. In the gradient flow case, we prove the followin…