Fractal approximation of Jackson type for periodic phenomena

Navascués, M.A. (Universidad de Zaragoza) ; Jha, S. ; Chand, A.K.B. ; Sebastián, M.V.

Resumen: The reconstruction of an unknown function providing a set of Lagrange data can be approached by means of fractal interpolation. The power of that methodology allows us to generalize any other interpolant, both smooth and nonsmooth, but the important fact is that this technique provides one of the few methods of nondifferentiable interpolation. In this way, it constitutes a functional model for chaotic processes. This paper studies a generalization of an approximation formula proposed by Dunham Jackson, where a wider range of values of an exponent of the basic trigonometric functions is considered. The trigonometric polynomials are then transformed in close fractal functions that, in general, are not smooth. For suitable election of this parameter, one obtains better conditions of convergence than in the classical case: the hypothesis of continuity alone is enough to ensure the convergence when the sampling frequency is increased. Finally, bounds of discrete fractal Jackson operators and their classical counterparts are proposed.

Idioma: Inglés

DOI: 10.1142/S0218348X18500792

Año: 2018

Publicado en: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 26, 5 (2018), 1850079 [14 pp]
ISSN: 0218-348X

Factor impacto JCR: 2.971 (2018)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 15 / 105 = 0.143 (2018) - Q1 - T1
Categ. JCR: MULTIDISCIPLINARY SCIENCES rank: 18 / 69 = 0.261 (2018) - Q2 - T1

Factor impacto SCIMAGO: 0.556 - Applied Mathematics (Q1) - Multidisciplinary (Q1) - Modeling and Simulation (Q1) - Geometry and Topology (Q1)

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)