文章基本信息

标题：Rational iterated function system for positive/monotonic shape preservation
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作者：AKB Chand ; N Vijender ; RP Agarwal 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：30
DOI：10.1186/1687-1847-2014-30
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper we consider the (inverse) problem of determining the iterated function system (IFS) which produces a shaped fractal interpolant. We develop a new type of rational IFS by using functions of the form E i F i , where E i are cubics and F i are preassigned quadratics having 3-shape parameters. The fixed point of the developed rational cubic IFS is in C 1 , but its derivative varies from a piecewise differentiable function to a continuous nowhere differentiable function. An upper bound of the uniform error between the fixed point of a rational IFS and an original function Φ ∈ C 4 is deduced for the convergence results. The automatic generations of the scaling factors and shape parameters in the rational IFS are formulated so that its fixed point preserves the positive/monotonic features of prescribed data. The presence of scaling factors provides additional freedom to the shape of the fractal interpolant over its classical counterpart in the modeling of discrete data.
关键词：Shape Parameter ; Original Function ; Unique Fixed Point ; Iterate Function System ; Uniform Error