Monotonicity Preserving Rational Quadratic Fractal Interpolation Functions. (30th January 2014)

• Record Type: Journal Article
• Authors: Chand, A. K. B.; Vijender, N.
• Other Names: Safouhi Hassan Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2014(2014)
• Publication Date: 2014-01-30
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2014/504825
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : Fractal interpolation is an advanced technique for analysis and synthesis of scientific and engineering data. We introduce the𝒞 1 -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 preserving𝒞 1 -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 in𝒞 4 . 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.