Examinando por Materia "FUNCIONES ANALÍTICAS"
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Ítem Fitting of Analytic Surfaces to Noisy Point Clouds(Scientific Research Publishing, 2013-04) Ruíz, Óscar; Arroyave, Santiago; Acosta, Diego; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEFitting -continuous or superior surfaces to a set of points sampled on a 2-manifold is central to reverse engi- neering, computer aided geometric modeling, entertaining, modeling of art heritage, etc -- This article addresses the fit- ting of analytic (ellipsoid, cones, cylinders) surfaces in general position in -- Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimat- ing the geometric distance between a point of and the analytic surface SF -- These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set -- In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids -- A conjecture for the calculation of the distance point-ellipsoid is also proposed -- Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm -- Ongoing work addresses the fitting of free-form parametric surfaces to SÍtem Limits of quotients of bivariate real analytic functions(ELSEVIER, 2013-03) Molina, Sergio; Cadavid Moreno, Carlos Alberto; Vélez Caicedo, Juan Diego; Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones; Carlos Cadavid M.(ccadavid@eafit.edu.co); Análisis Funcional y AplicacionesNecessary and sufficient conditions for the existence of limits of the form lim(x,y)→(a,b) f (x, y)/g(x, y) are given, under the hypothesis that f and g are real analytic functions near the point (a, b), and g has an isolated zero at (a, b) -- The given criterion uses a constructive version of Hensel’s Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials with rational coefficients, or more generally, with coefficients in a real finite extension of the rationals -- A high level description of an algorithm for determining the existence of the limit as well as its computation is providedÍtem A q-exponential statistical Banach manifold(ELSEVIER, 2013-02) Quiceno Echavarría, Héctor Román; Loaiza Ossa, Gabriel Ignacio; department:Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones; Héctor R. Quiceno (hquiceno@eafit.edu.co); Gabriel Loaiza (gloaiza@eafit.edu.co); Análisis Funcional y AplicacionesLetµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function