Book ChapterDOI
$$\mathbf {}$$-Fractal Rational Functions and Their Positivity spects
S. K. Katiyar,A. K. B. Chand +1 more
- pp 205-215
TLDR
In this article, a general construction of fractal rational functions is introduced for the first time in the literature, which allows to insert shape parameters for positivity-preserving univariate interpolation.Abstract:
Coalescence hidden variable fractal interpolation function (CHFIF) proves more versatile than classical interpolant and fractal interpolation function (FIF). Using rational functions and CHFIF, a general construction of \(\mathbf {A}\)-fractal rational functions is introduced for the first time in the literature. This construction of \(\mathbf {A}\)-fractal rational function also allows us to insert shape parameters for positivity-preserving univariate interpolation. The convergence analysis of the proposed scheme is established. With suitably chosen numerical examples and graphs, the effectiveness of the positivity-preserving interpolation scheme is illustrated.read more
Citations
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Journal ArticleDOI
Fractal Curves on Banach Algebras
TL;DR: In this article, the construction of fractal curves with values in abstract settings such as Banach spaces and algebras, with minimal conditions and structures, transcending in this way the numerical underlying scenario, is performed via fixed point of an operator defined on a b-metric space of Banachvalued functions with domain on a real interval.
References
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Journal ArticleDOI
Monotone Piecewise Cubic Interpolation
F. N. Fritsch,R. E. Carlson +1 more
TL;DR: In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.
Journal ArticleDOI
Fractal Functions and Interpolation
TL;DR: In this article, the authors introduce iterated function systems whose attractorsG are graphs of continuous functionsf∶I→R, which interpolate the data according tof(x��i)=y fixmei fori e {0,1,⋯,N}.
Book
Fractal functions, fractal surfaces, and wavelets
TL;DR: Fractal Function Wavelet theory as mentioned in this paper is a well-known extension of the basic wavelet theory and has been applied to the construction of Fractal Sets as Fractal Functions and Fractal Surfaces.
Journal ArticleDOI
The calculus of fractal interpolation functions
TL;DR: The calculus of deterministic fractal functions is introduced in this article, which can be explicitly indefinitely integrated any number of times, yielding a hierarchy of successively smoother interpolation functions which generalize splines and which are attractors for iterated function systems.
Journal ArticleDOI
Hidden variable fractal interpolation functions
TL;DR: In this article, the authors constructed interpolation functions of the form f[0, 1] \to \mathbb{R}$ of the following nature: given data, f obeys the following properties: f(t_n ) = x_n,\qquad n = 0,1,2, \cdots,N.
Related Papers (5)
Toward a Unified Methodology for Fractal Extension of Various Shape Preserving Spline Interpolants
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Constrained univariate and bivariate rational fractal interpolation
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