SHAPE PRESERVING RATIONAL QUARTIC FRACTAL FUNCTIONS

作     者：Katiyar, S. K. Chand, A. K. B. 

作者机构：SRM Inst Sci & Technol Dept Math Chennai 603203 Tamil Nadu India Indian Inst Technol Madras Chennai 600036 Tamil Nadu India 

出 版 物：《FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY》 (分数；自然复几何多学科杂志)

年 卷 期：2019年第27卷第8期

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Fractals Iterated Function System Fractal Interpolation Functions Positivity Monotonicity Convexity 

摘      要：The appearance of fractal interpolation function represents a revival of experimental mathematics, raised by computers and intensified by powerful evidence of its applications. This paper is devoted to establish a method to construct alpha-fractal rational quartic spline, which eventually provides a unified approach for the generalization of various traditional nonrecursive rational splines involving shape parameters. We deduce the uniform error bound for the alpha-fractal rational quartic spline when the original function is in C-4(J). By solving a system of linear equations, appropriate values of the derivative parameters are determined so as to enhance the continuity of the alpha-fractal rational quartic spline to C-2. The elements of the iterated function system are identified befittingly so that the class of alpha-fractal function Q(alpha) incorporates the geometric features such as positivity, monotonicity and convexity in addition to the regularity inherent in the germ Q. This general theory in conjunction with shape preserving aspects of the traditional splines provides algorithms for the construction of shape preserving fractal interpolation functions.