Related papers: Chebyshev centers and radii for sets induced by qu…
The Chebyshev set of a bounded set $K$ in a normed space is the set of centers of all minimal enclosing balls of $K$. We use the concept of ball intersection and ball hull operators to derive new properties of Chebyshev sets in normed…
We study the n-dimensional problem of finding the smallest ball enclosing the intersection of p given balls, the so-called Chebyshev center problem (CCB). It is a minimax optimization problem and the inner maximization is a uniform…
Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center…
We study the metric geometry of the set of permutons under the rectangular distance $d_{\square}$. We determine the Chebyshev radius to be 1/4 and characterize all Chebyshev centers: a permuton is a center if and only if it is 1/2- periodic…
This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution…
In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and radius of open/closed balls. The center and radius of a…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains $G\subsetneq\mathbb{R}^n$. The already known inequalities between the hyperbolic metric and…
In this article, we study the approximate solutions set $\Lambda_b$ of an inconsistent system of $\max-\min$ fuzzy relational equations $(S): A \Box_{\min}^{\max}x =b$. Using the $L_\infty$ norm, we compute by an explicit analytical formula…
For a bounded metric space $ X $ one can consider the quantity $ \delta(X) := \text{inf\rule[-0.5ex]{0em}{1ex}}_{\,p\in X}\; \text{sup}_{q \in X} \; d(p,q) $. This purely metric invariant is known from approximation theory as the relative…
In this paper we address the question whether in a given Banach space, a Chebyshev center of a nonempty bounded subset can be a farthest point of the set. Our exploration reveals that the answer depends on the convexity properties of the…
A Chebyshev-type quadrature for a probability measure sigma is a distribution which is uniform on n points and has the same first k moments as sigma. We give an upper bound for the minimal n required to achieve a given degree k, for sigma…
This paper deals with the containment problem under homothetics which has the minimal enclosing ball (MEB) problem as a prominent representative. We connect the problem to results in classic convex geometry and introduce a new series of…
Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…
We analyze decay of Chebyshev coefficients and local Chebyshev approximations for functions of finite regularity on finite intervals, focusing on the framework where the interval length tends to zero while the number of approximation nodes…
We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in…
Uniform polynomial approximation, also called minimax approximation or Chebyshev approximation, consists in searching polynomial approximation that minimizes the worst case error. Optimality conditions for the uniform approximation of…
In this paper we study the following problems: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects…
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the…
We prove a randomized version of the generalized Urysohn inequality relating mean-width to the other intrinsic volumes. To do this, we introduce a stochastic approximation procedure that sees each convex body K as the limit of intersections…