We discuss and compare two greedy algorithms, that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called “Approximate Fekete Points” by QR factorization with column pivoting of Vandermonde-like matrices. The second computes Discrete Leja Points by LU factorization with row pivoting. Moreover, we st...

The objective of this work is to provide a methodology for approximating globally optimal Fekete point con-gurations. This problem is of obvious interest in numerical mathematics and scientic modeling. Following a brief discussion of the pertinent analytical background, Lipschitz global optimization (LGO) is applied to determine {i.e., to numerically approximate{ Fekete point congurations. Next...

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-...

A new class of point-interaction problem characterizing the time evolution of spatially localized spots for reaction-diffusion (RD) systems on the surface of the sphere is introduced and studied. This problem consists of a differential algebraic system (DAE) of ODE’s for the locations of a collection of spots on the sphere, and is derived from an asymptotic analysis in the large diffusivity rat...

In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′(z) (1− λ)f(z) + λzf ′(z) (0 ≤ λ < 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are giv...

The main purpose of our work is to provide Fekete and Lebesgue points on three basic bidimensional compact sets, the simplex, the square, and the disk, by solving numerically the corresponding large-scale nonlinear optimization problems up to degree n = 18. Our results reach and often improve those previously known [1], [3]. In the case of the simplex, due to their relevance in developing spect...

It is known that if x is a real residue character modulo k with x(p) = — 1 k n for the first five primes p, then the corresponding Fekete polynomial £„=j X(n)x changes sign on (0, 1). In this paper it is shown that the condition that x(p) be — 1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if x ¡s the real nonprincipal character modulo either...