Fractal perturbation preserving fundamental shapes: Bounds on the scale factors

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:419

Article

Viswanathan, P.¹  Chand, A. K. B.¹  Navascues, M. A.² 

[1] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India

[2] Univ Zaragoza, Escuela Ingn & Arquitectura, Dept Matemat Aplicada, Zaragoza 50018, Spain

关键词: alpha-Fractal function;    Fractals;    Shape preserving approximation;    Muntz polynomial;   

DOI  :  10.1016/j.jmaa.2014.05.019

来源: Elsevier

【 摘 要 】

Fractal interpolation function defined through suitable iterated function system provides a method to perturb a function f is an element of C(I) so as to yield a class of functions f(alpha) is an element of C(I), where a is a free parameter, called scale vector. For suitable values of scale vector alpha, the fractal functions f(alpha) simultaneously interpolate and approximate f. Further, the iterated function system can be selected suitably so that the corresponding fractal function f(alpha) shares the quality of smoothness or non-smoothness of f. The objective of the present paper is to choose elements of the iterated function system appropriately in order that f(alpha) preserves fundamental shape properties, namely positivity, monotonicity, and convexity in addition to the regularity of f in the given interval. In particular, the scale factors (elements of the scale vector) must be restricted to satisfy two inequalities that provide numerical lower and upper bounds for the multipliers. As a consequence of this process, fractal versions of some elementary theorems in shape preserving interpolation/approximation are obtained. For instance, positive approximation (that is to say, using a positive function) is extended to the fractal case if the factors verify certain inequalities. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free