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-...

This paper deals with Vandermonde matrices V whose nodes are the equidistant points in [0,1]. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both V and its inverse and show that a new representation of the floating point number system allows one to build an ...

Although Gaussian elimination uses O(n) operations to invert an arbitrary matrix, matrices with a special Vandermonde structure can be inverted in only O(n) operations by the fast Traub algorithm. The original version of Traub algorithm was numerically unstable although only a minor modification of it yields a high accuracy in practice. The Traub algorithm has been extended from Vandermonde mat...

A property is called persistent if for any manysorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that termination is persistent for locally confluent overlay term rewriting systems and we give the example as application of this result. Furthermore we obtain that co...

The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function introduce $τ$-Gauss hypergeometric and $τ$-confluent functions with some their properties, such as Laplace-type Euler-type integral formulas. Another apply them fractional kinetic equations that appear in astrophysics physics using Laplace transform method.

Jungles are acyclic hypergraphs which represent sets of terms such that common subterms can be shared. Term rewrite rules are translated into jungle evaluation rules which implement parallel term rewriting steps. By using additional hypergraph rules which “fold” equal subterms, even non-left-linear term rewriting systems can be implemented. As a side effect, these folding rules can speed up the...

We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the “sampling problem for trigonometric polynomials”) and estimate the probability distribution of the condition number for the associated Vandermonde-type and Toeplitz-like matrices. The results provide a solid theoretical...

An account of the basic theory of confluence in the 1r-calculus is presented, techniques for showing confluence of mobile systems are given, and the utility of some of the theory presented is illustrated via an analysis of a distributed algorithm. 1 I n t r o d u c t i o n Confluence arises in a variety of forms in computation theory. It was first studied in the context of concurrent systems by...