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Title
Abstract
Key Takeaways
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Introduction
Conclusions
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Mathematics
Functional Analysis

A Method of Curve Fitting by Recurrent Fractal Interpolation

Profile image of Kuldip KatiyarKuldip Katiyar

2012

Abstract

The real world objects are too irregular to be modeled with the help of traditional interpolation methods. M. F. Barnsley in 1986 proposed the concept of fractal interpolation function (FIF) using iterated function systems (IFS) to describe such real world data. In many cases these data sets represent a curve rather than a function i.e. the data points are not linearly ordered with their abscissa and self affinity is not satisfied in the whole range. The recurrent fractal interpolation function (RFIF) has a role to play in such cases. The purpose of this paper is to apply recurrent fractal interpolation function to fit the piecewise self affine data.

Key takeaways
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  1. The recurrent fractal interpolation function (RFIF) effectively fits piecewise self-affine data sets.
  2. Fractal interpolation differs from traditional methods by using iterated function systems (IFS).
  3. The algorithm selects best matching sections and calculates contractivity factors via least squares.
  4. Data points can represent curves, complicating application of standard fractal interpolation techniques.
  5. This study enhances modeling capabilities for irregular natural objects like coastlines and plants.
Figures (2)
The constants are chosen such that each map w,, is constrained to map the endpoints of the section S,, to the endpoints of the interval /,,. That is, International Conference in Computational Intelligence (ICCIA) 2011 roceedings published in International Journal of Computer Applications® (IJCA)
The constants are chosen such that each map w,, is constrained to map the endpoints of the section S,, to the endpoints of the interval /,,. That is, International Conference in Computational Intelligence (ICCIA) 2011 roceedings published in International Journal of Computer Applications® (IJCA)
International Conference in Computational Intelligence (ICCIA) 201, -roceedings published in International Journal of Computer Applications® (IJCA, 4. CONCLUSIONS
International Conference in Computational Intelligence (ICCIA) 201, -roceedings published in International Journal of Computer Applications® (IJCA, 4. CONCLUSIONS

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References (20)

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  20. Uemura, S., Haseyama, M., and Kitajima, H. 2002. Efficient contour shape description by using fractal interpolation functions. IEEE Proc. ICIP. 1, 485-488.

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