Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Sonnleitner, Mathias"'
The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between finite-dimensional Lorentz
Externí odkaz:
http://arxiv.org/abs/2404.06058
While there is extensive literature on approximation, deterministic as well as random, of general convex bodies $K$ in the symmetric difference metric, or other metrics arising from intrinsic volumes, very little is known for corresponding random res
Externí odkaz:
http://arxiv.org/abs/2404.02870
Autor:
Sonnleitner, Mathias, Ullrich, Mario
Publikováno v:
JANA 1 (2023) 88-126
This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed (iid) at rand
Externí odkaz:
http://arxiv.org/abs/2310.12740
Autor:
Sonnleitner, Mathias, Thäle, Christoph
The purpose of this note is to study the asymptotic volume of intersections of unit balls associated with two norms in $\mathbb{R}^n$ as their dimension $n$ tends to infinity. A general framework is provided and then specialized to the following case
Externí odkaz:
http://arxiv.org/abs/2308.10635
Autor:
Sonnleitner, Mathias
Combination locks are widely used to secure bicycles. We consider a combination lock consisting of adjacent rotating dials with the first nonnegative integers printed on each of them. Assuming that we know the correct combination and we start from an
Externí odkaz:
http://arxiv.org/abs/2308.10321
We develop a probabilistic approach to study the volumetric and geometric properties of unit balls $\mathbb B_{q,1}^n$ of finite-dimensional Lorentz sequences spaces $\ell_{q,1}^n$. More precisely, we show that the empirical distribution of a random
Externí odkaz:
http://arxiv.org/abs/2303.04728
Autor:
Sonnleitner, Mathias
This thesis investigates the quality of randomly collected data by employing a framework built on information-based complexity, a field related to the numerical analysis of abstract problems. The quality or power of gathered information is measured b
Externí odkaz:
http://arxiv.org/abs/2209.07266
Autor:
Krieg, David, Sonnleitner, Mathias
Publikováno v:
In Journal of Approximation Theory January 2025 305
Publikováno v:
In Journal of Functional Analysis 1 January 2025 288(1)
We study the circumradius of a random section of an $\ell_p$-ellipsoid, $0
Externí odkaz:
http://arxiv.org/abs/2109.14504