47 citations · 123 across the 18 of their papers we have counts for
22 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…
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.
Limitations on approximation by deep and shallow neural networks
Guergana Petrova, Przemysław Wojtaszczyk
We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives lower bounds on how well we can approxima…
Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including Besov spaces
Fernando Albiac, José L. Ansorena, Glenier Bello +1
We prove that the sequence spaces and the spaces of infinite matrices , and , whic…
On the entropy numbers and the Kolmogorov widths
Guergana Petrova, Przemyslaw Wojtaszczyk
Direct estimates between linear or nonlinear Kolmogorov widths and entropy numbers are presented. These estimates are derived using the recently introduced Lipschitz widths. Applic…
Lipschitz widths
Guergana Petrova, Przemyslaw Wojtaszczyk
This paper introduces a measure, called Lipschitz widths, of the optimal performance possible of certain nonlinear methods of approximation. It discusses their relation to entropy…