4 papers · 1 filter
Greedy sparsifications of sums of positive semidefinite matrices
Grigory Ivanov
We prove a deterministic analogue of Rudelson's sampling theorem for sums of positive semidefinite matrices. Let be positive semidefinite \(d\times d\) matrices, an…
On Banach Spaces with the Helly Approximation Property
Grigory Ivanov
Qualitatively, a no-dimensional Helly-type theorem says that if every small subfamily of convex sets has a common point in a bounded region, then suitable neighborhoods of all the…
No-dimensional results of combinatorial convexity. Dimension strikes back
Grigory Ivanov
We discuss no-dimensional (approximate) versions of Carathéodory's and Helly's theorems. Our goal is to draw attention to open problems and potential applications related to these…
No-dimensional Helly's theorem in uniformly convex Banach spaces
G. Ivanov
We study the ``no-dimensional'' analogue of Helly's theorem in Banach spaces. Specifically, we obtain the following no-dimensional Helly-type results for uniformly convex Banach sp…