Results 181 to 190 of about 5,604,790 (214)

Fractal Multiquadric Interpolation Functions

SIAM Journal on Numerical Analysis
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D. Kumar, A. K. B. Chand, Peter R. Massopust   +2 more
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FOURIER SERIES REPRESENTATION OF FRACTAL INTERPOLATION FUNCTION

Fractals, 2020
The purpose of this research is to show how the complicated and irregular fractal interpolation function is represented by Fourier series. First, on the closed interval [0,1], even prolongation is operated to the fractal interpolation function generated by iterated function system constituted by affine transform and Fourier cosine series ...
XUEZAI PAN, MINGGANG WANG, XUDONG SHANG
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Generalized Cubic Spline Fractal Interpolation Functions

SIAM Journal on Numerical Analysis, 2006
We construct a generalized Cr-Fractal Interpolation Function (Cr-FIF) f by prescribing any combination of r values of the derivatives f(k), k=1,2,\dots,r, at boundary points of the interval I = [x0,xN]. Our approach to construction settles several questions of Barnsley and Harrington [J. Approx Theory, 57 (1989), pp.
Arya Kumar Bedabrata Chand, G P Kapoor
exaly   +3 more sources

Fractal functions and interpolation

Constructive Approximation, 1986
Consider a set of data points \(\{x_ i,y_ i)\in I\times R:i=0,...,N\}\), where \(I=[x_ 0,x_ N]\subseteq R\). The author considers continuous functions f:I\(\to R\) which interpolate the given data, i.e. \(f(x_ i)=y_ i\), and such that there exist a compact subset \(K=I\times [a,b]\subseteq R^ 2\) and continuous functions \(w_ n:K\to K\) such that the ...
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Holder property of fractal interpolation function

Approximation Theory and its Applications, 1992
Summary: The purpose of this paper is to prove a Hölder property about the fractal interpolation function \(L(x)\), \(\omega(L,\delta)=O(\delta^ \alpha)\), and an approximate estimate \(| f-L|\leq 2\{\omega(h)+{{\| f\|} \over {1-h^{2-D}}}\cdot h^{2-D}\}\), where \(D\) is a fractal dimension of \(L(x)\).
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3D Fractal Interpolation Functions

Nanoscience and Nanotechnology Letters, 2020
For visualizing one, two- and/or three-dimensional data, reconstruction mechanism is generally considered. In the present study, I have examined the application of iterated function systems in interpolation. I have also presented new fractal interpolation derivations for three-dimensional scalar data. The interpolations can indicate uncertainty of the
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REVIEW ON FRACTAL INTERPOLATION FUNCTIONS

Fractals
The idea of fractal interpolation dates back to the 1980s, however several recent developments on its new types and generalization frameworks have made this domain ripe for extensions, further analyses, and reliable applications. Commencing from the background of Barnsley’s fundamental fractal interpolation function, this review paper summarizes the ...
T. M. C. PRIYANKA, A. GOWRISANKAR
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Zipper Rational Quadratic Fractal Interpolation Functions

2020
Inthis article, we propose an interpolation method using a binary parameter called signature such that the graph of the interpolant is an attractor of a suitable zipper rational iterated function system. The presence of scaling factors and signature in the proposed zipper rational quadratic fractal interpolation functions (ZRQFIFs) gives the ...
Sangita Jha, A. K. B. Chand
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A TYPE OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR FRACTIONAL CALCULUS

Fractals, 2016
Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann–Liouville fractional calculus and Box dimension of FIF has been ...
Liang, Yong-Shun, Zhang, Qi
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Fractal Interpolation Function for Countable Data

2020
The problem of extending the theory of an iterated function system carried over to an infinite and countable iterated function system has been widely studied in the last decades. Such an extension is applied in the theory of sampling and reconstruction where a countable iterated function system contributes to a better approximation.
Santo Banerjee, D. Easwaramoorthy, A. Gowrisankar   +2 more
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