Table of Contents
Advances in Numerical Analysis
Volume 2014, Article ID 504825, 17 pages
http://dx.doi.org/10.1155/2014/504825
Research Article

Monotonicity Preserving Rational Quadratic Fractal Interpolation Functions

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India

Received 4 June 2013; Accepted 13 October 2013; Published 30 January 2014

Academic Editor: Hassan Safouhi

Copyright © 2014 A. K. B. Chand and N. Vijender. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fractal interpolation is an advanced technique for analysis and synthesis of scientific and engineering data. We introduce the -rational quadratic fractal interpolation functions (FIFs) through a suitable rational quadratic iterated function system (IFS). The novel notion of shape preserving fractal interpolation without any shape parameter is introduced through the rational fractal interpolation model in the literature for the first time. For a prescribed set of monotonic data, we derive the sufficient conditions by restricting the scaling factors for shape preserving -rational quadratic FIFs. A local modification pertaining to any subinterval is possible in this model if the scaling factors are chosen appropriately. We establish the convergence results of a monotonic rational quadratic FIF to the original function in . For given data with derivatives at grids, our approach generates several monotonicity preserving rational quadratic FIFs, whereas this flexibility is not available in the classical approach. Finally, numerical experiments support the importance of the developed rational quadratic IFS scheme through construction of visually pleasing monotonic rational fractal curves including the classical one.