Rocky Mountain Journal of Mathematics

Constrained shape preserving rational cubic fractal interpolation functions

A.K.B. Chand and K.R. Tyada

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Abstract

In this paper, we discuss the construction of $\mathcal {C}^1$-rational cubic fractal interpolation function (RCFIF) and its application in preserving the constrained nature of a given data set. The $\mathcal {C}^1$-RCFIF is the fractal design of the traditional rational cubic interpolant of the form ${p_i(\theta )}/{q_i(\theta )}$, where $p_i(\theta )$ and $q_i(\theta )$ are cubic and quadratic polynomials with three tension parameters. We present the error estimate of the approximation of RCFIF with the original function in $\mathcal {C}^k[x_1,x_n]$, $k=1,3$. When the data set is constrained between two piecewise straight lines, we derive the sufficient conditions on the IFS parameters of the RCFIF so that it lies between those two lines. Numerical examples are given to support the theoretical results.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 1 (2018), 75-105.

Dates
First available in Project Euclid: 28 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1524880882

Digital Object Identifier
doi:10.1216/RMJ-2018-48-1-75

Mathematical Reviews number (MathSciNet)
MR3795734

Zentralblatt MATH identifier
06866701

Subjects
Primary: 28A80: Fractals [See also 37Fxx] 37C25: Fixed points, periodic points, fixed-point index theory 41A30: Approximation by other special function classes 41A55: Approximate quadratures 42A15: Trigonometric interpolation

Keywords
Iterated function systems fractal interpolation convergence analysis bounding Cauchy remainder Peano-kernel theorem constrained data interpolation positivity

Citation

Chand, A.K.B.; Tyada, K.R. Constrained shape preserving rational cubic fractal interpolation functions. Rocky Mountain J. Math. 48 (2018), no. 1, 75--105. doi:10.1216/RMJ-2018-48-1-75. https://projecteuclid.org/euclid.rmjm/1524880882


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