Related papers: On Fekete Points for a Real Simplex
In this paper we discuss equidistribution results for weighted Fekete sets in subsets of the plane. More precisely, we show that Fekete sets are maximally spread out relative to a rescaled version of the Beurling--Landau density, in the…
A first order form of Regge calculus is defined in the spirit of Palatini's action for general relativity. The extra independent variables are the interior dihedral angles of a simplex, with conjugate variables the areas of the triangles.…
We introduce the theory of div point sets, which aims to provide a framework to study the combinatoric nature of any set of points in general position on an Euclidean plane. We then show that proving the unsatisfiability of some first-order…
We present new pivot rules for the Simplex method for LPs over 0/1 polytopes. We show that the number of non-degenerate steps taken using these rules is strongly polynomial and even linear in the dimension or in the number of variables. Our…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation { transforming the original…
Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…
In this note, we obtain the growth order of Lebesgue constants for Fekete points associated with tensor powers of a positive line bundle. Moreover, by endowing the space of global holomorphic sections with a natural Gaussian probability…
We investigate some combinatorial properties of convex polytopes simple in edges. For polytopes whose nonsimple vertices are located sufficiently far one from another, we prove an analog of the Hard Lefschetz theorem. It implies Stanley's…
We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for…
We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated…
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
In this paper, we propose a new general and stable fixed-point approach to compute the resolvents of the composition of a set-valued maximal monotone operator with a linear bounded mapping. Weak, strong and linear convergence of the…
Using Semaev's summation polynomials, we derive a new equation for the $\mathbb{F}_q$-rational points of the trace zero variety of an elliptic curve defined over $\mathbb{F}_q$. Using this equation, we produce an optimal-size representation…
We use methods from computational algebraic geometry to study Chebyshev constants and the transfinite diameter of a pure $m$-dimensional affine algebraic variety in $\mathbb{C}^n$ ($m\leq n$). The main result is a generalization of…
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…
We construct finite element de~Rham complexes of higher and possibly non-uniform polynomial order in finite element exterior calculus (FEEC). Starting from the finite element differential complex of lowest-order, known as the complex of…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
We determine upper bounds on the number of rational points of an affine or projective algebraic set defined over an extension of a finite field by a system of polynomial equations, including the case where the algebraic set is not defined…