6 papers · 1 filter
Gradient descent with exponentially increasing stepsizes and restarts
François Clément, Stefan Steinerberger
Let . We consider gradient descent , where the stepsize is exponentially growing (wi…
A Remark on the Odd Area of Unit Disks
Stefan Steinerberger
Let be a family of unit disks in with being odd. We use $\mbox{OA}(F)$ to denote the area of the set of points that is covered by an odd number of disks.…
An effective variant of the Hartigan -means algorithm
François Clément, Stefan Steinerberger
The k-means problem is perhaps the classical clustering problem and often synonymous with Lloyd's algorithm (1957). It has become clear that Hartigan's algorithm (1975) gives bette…
Buffon Discrepancy and the Steinhaus Longimeter
Stefan Steinerberger
Let be a convex set. We study the problem of distributing a one-dimensional set with total length so that for any line in the…
Slow dispersion in Floquet-Dirac Hamiltonians
Anthony Bloch, Amir Sagiv, Stefan Steinerberger
We study dispersive decay for non-autonomous Hamiltonian systems. While the general theory for dispersion in such non-autonomous systems is largely open, it was shown \cite{kraisle…
Distance Equilibrium Measures and Curvature in Metric Spaces
Stefan Steinerberger
Let be a compact metric space. We consider the behavior of probability measures with the property that $$ \int_{X} d(x, y) dμ(y) \qquad \mbox{is independent of}~x \in X…