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
