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Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new -point transformation that yields a function with a simpler geometrical structure than the original function. It uses reference points and decreases the polynomial degree by . Then a general representation of polynomials is proposed based on reference...
We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions is estimated. Markov’s constants of the corresponding set are evaluated.
El objeto del trabajo es la determinación de una cota superior del número real ρ definido comoρ = límn→∞ ρn ρn-n = MinPn∈Hn Max0≤x≤1 |Pn(X)|H n clase de polinomios no nulos con coeficientes en Z y grado menor o igual a n.En un artículo anterior (RMHA, 4 serie, t. XXXVIII, nº 6, 1978, pp. 259-270) el autor muestra que dado (λ1,...,λn) sistema completo de números reales algebraicos y algebraicamente conjugados, verificando:0 ≤ 1/λi+s ≤ 1 ∀i, ∃ s ∈ Zy definiendoδ = (∏i=1m |λi+s|)1/mse verifica ρ...
Dans cet article nous améliorons des encadrements connus du diamètre transfini entier d’intervalles dont les bornes sont deux éléments consécutifs d’une suite de Farey. Nous verrons comment la majoration du diamètre transfini de tels intervalles dépend de la minoration de certaines mesures de polynômes unitaires, à coefficients entiers et totalement positifs, mesures qui généralisent la longueur usuelle. D’autre part, appliquant un lemme classique sur les résultants à une famille de polynômes totalement...
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