scholarly journals New Approach to Fractal Approximation of Vector-Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Konstantin Igudesman ◽  
Marsel Davletbaev ◽  
Gleb Shabernev
Keyword(s):  
Fractal Interpolation ◽  
New Approach ◽  
Smooth Curves ◽  
Continuous Vector ◽  
Multidimensional Generalization ◽  
Fractal Interpolation Functions ◽  
Fractal Approximation ◽  
Vector Sequences ◽  
Interpolation Functions

This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.

scholarly journals A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 767
Author(s):  
Alexandra Băicoianu ◽  
Cristina Maria Păcurar ◽  
Marius Păun
Keyword(s):  
Approximation Method ◽  
Finite System ◽  
Countable System ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Finite Systems ◽  
Fractal Interpolation Function ◽  
Fractal Interpolation Functions ◽  
Finite Set ◽  
Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .

CONSTRUCTING MULTIPLE WAVELET PACKETS WITH FIFS

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 165-169
Author(s):  
GANG CHEN ◽  
ZHIGANG FENG
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Wavelet Packet Decomposition ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

By using fractal interpolation functions (FIF), a family of multiple wavelet packets is constructed in this paper. The first part of the paper deals with the equidistant fractal interpolation on interval [0, 1]; next, the proof that scaling functions ϕ1, ϕ2,…,ϕr constructed with FIF can generate a multiresolution analysis of L2(R) is shown; finally, the direct wavelet and wavelet packet decomposition in L2(R) are given.

SURFACE FITTING AND ERROR ANALYSIS USING FRACTAL INTERPOLATION

2012 ◽  
Vol 22 (08) ◽  
pp. 1250194 ◽  
Author(s):  
HONG-YONG WANG ◽  
JIA-BING JI
Keyword(s):  
Error Analysis ◽  
Iterated Function Systems ◽  
Surface Fitting ◽  
Continuous Functions ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Iterated Function ◽  
Continuous Surface ◽  
Fractal Interpolation Surface ◽  
Interpolation Functions

The fitting of a given continuous surface defined on a rectangular region in ℝ2 is studied by using a fractal interpolation surface, and the error analysis of fitting is made in this paper. The fractal interpolation functions used in surface fitting are generated by a special class of iterated function systems. Some properties of such fractal interpolation functions are discussed. Moreover, the error problems of fitting are investigated by using an operator defined on the space of continuous functions, and the upper estimates of errors are obtained in the sense of two kinds of metrics. Finally, a specific numerical example to illustrate the application of the procedure is also described.

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