Hidden-variable alpha-fractal functions and their monotonicity aspects.
Katiyar, Saurabh ; Chand, A.K. Bedabrata ; Navascués Sanagustín, María Antonia (Universidad de Zaragoza)
Resumen: Fractal interpolation that possesses the ability to produce smooth and nonsmooth inter- polants is a novice to the subject of interpolation. Apart from appropriate degree of smooth- ness, a good interpolant should reflect shape properties, for instance monotonicity, inherent in a prescribed data set. Despite the flexibility offered by these shape preserving fractal interpolants developed recently in the literature are well-suited only for the representation of self-referential functions. In this article we present hidden variable A-fractal interpo- lation function as a tool to associate an entire family of R2-valued continuous functions f[A] parameterized by a suitable block matrix A with a prescribed function f ¿ C(I,R2). Depending on the choice of parameters, the members of the family may be self-referential, or non-self-referential, and preserve some properties of original function f, thus yielding more diversity and flexibility in the process of approximation. As an application of the developed theory, we introduce a new class of monotone C1-cubic interpolants by taking full advantage of flexibility offered by the hidden variable A-fractal interpolation functions (HFIFs). This theory invoked to the C1-cubic spline HFIF, which can be viewed as a fractal perturbation of the traditional C1-cubic spline, culminates with the desired monotonicity preserving C1-cubic HFIF. The monotonicity preserving interpolation scheme developed herein generalizes and enriches its traditional nonrecursive counterpart and its fractal ex- tension.
Idioma: Inglés
Año: 2016
Publicado en: Revista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza 71 (2016), 7-30
ISSN: 0370-3207
Tipo y forma: Article (Published version)
Área (Departamento): Matemática Aplicada (Departamento de Matemática Aplicada)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes.
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Idioma: Inglés
Año: 2016
Publicado en: Revista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza 71 (2016), 7-30
ISSN: 0370-3207
Tipo y forma: Article (Published version)
Área (Departamento): Matemática Aplicada (Departamento de Matemática Aplicada)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. Exportado de SIDERAL (2017-02-17-11:08:12)
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Record created 2017-02-17, last modified 2017-02-17