Journal ArticleDOI
Constrained shape preserving rational cubic fractal interpolation functions
A. K. B. Chand,K. R. Tyada +1 more
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In this article, the authors discuss the construction of a rational cubic fractal interpolation function (RCFIF) and its application in preserving the constrained nature of a given data set.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.read more
Citations
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Journal ArticleDOI
Shape preserving $$\alpha$$ α -fractal rational cubic splines
TL;DR: In this article, a new rational cubic spline is introduced with the help of the iterated function system (IFS) that contains rational functions, and the convergence analysis is established.
Journal ArticleDOI
Shape preserving rational cubic trigonometric fractal interpolation functions
TL;DR: A new family of C 1 -rational cubic trigonometric fractal interpolation functions (RCTFIFs) that are the generalized fractal version of the classical rational cubic trig onometric polynomial spline of the form p i ( θ ) ∕ q i (θ ) , where p i and q i are cubic trigonal polynomials with four shape parameters in each sub-interval.
Journal ArticleDOI
Fractal Perturbation of the Nadaraya–Watson Estimator
Dah-Chin Luor,Chiao-Wen Liu +1 more
TL;DR: In this paper , a fractal perturbation f[m^] corresponding to m^ is constructed to fit the given data, and the expectation for the expectation of |m^−m|2 is established.
Journal ArticleDOI
Constrained and convex interpolation through rational cubic fractal interpolation surface
TL;DR: In this paper, a new rational cubic fractal interpolation surface is introduced to interpolate the surface data which lies on a rectangular grid, where the scaling factors and the shape parameters are constrained.
Book ChapterDOI
Monotonicity Preserving Rational Cubic Graph-Directed Fractal Interpolation Functions.
A. K. B. Chand,K. M. Reddy +1 more
TL;DR: This work proposes a new class \(\mathscr {C}^1\)-rational cubic graph-directed FIFs (RCGDFIFs) using cubic rational function involving two shape parameters in each sub-interval and deduced sufficient condition based on the restriction of the corresponding rational GDIFS parameters.
References
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Journal ArticleDOI
A Method for Constructing Local Monotone Piecewise Cubic Interpolants
F. N. Fritsch,J. Butland +1 more
TL;DR: In this paper, a method for producing monotone piecewise cubic interpolants to monotonous data is described, which is completely local and which is extremely simple to implement.
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.
Journal ArticleDOI
Positivity of cubic polynomials on intervals and positive spline interpolation
Jochen W. Schmidt,Walter Heb +1 more
TL;DR: In this paper, a criterion for the positivity of a cubic polynomial on a given interval is derived, and a necessary and sufficient condition is given under which cubicC 1-spline interpolants are nonnegative.
Journal ArticleDOI
Shape Preserving Piecewise Rational Interpolation
R. Delbourgo,J. A. Gregory +1 more
TL;DR: In this article, an explicit representation of a piecewise rational cubic function is developed which can be used to solve the problem of shape preserving interpolation, and an error analysis of the interpolant is given.