We show that optimal polynomial meshes exist for every convex body in $${\mathbb {R}}^d$$ , confirming a conjecture by A. Kroó.

We prove large sieve inequalities with multivariate polynomial moduli and deduce a general Bombieri–Vinogradov type theorem for class of having sufficient number variables compared to its degree. This sharpens previous results the first author in two aspects: range as well polynomials which can be handled. As consequence, we that there exist infinitely many primes p such \(p-1\) has prime divis...

Abstract We discuss a pointwise numerical differentiation formula on multivariate scattered data, based the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s monomial basis. Error bounds for approximation partial derivatives any order compatible with function regularity are provided, as well sensitivity estimates to functional perturbations, terms inver...

In this paper, a remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated polynomial profiles, where there is a first order autoregressive (AR(1)) relation between the error terms in each profile. Then, a control chart based on the generalized linear test (GLT) is proposed to monitor the coefficients of polynomial profiles and an R-c...

The paper is concerned with the practical implementation of two methods to compute the solution of polynomial interpolation problems. In addition to a description of the implementation, practical results and several improvements will be discussed, focusing on speed and robustness of the algorithms under consideration.