ON THE BOUNDS OF SCALING FACTORS OF AFFINE FRACTAL INTERPOLATION FUNCTIONS

In this paper we obtain an upper bound and a lower bound for each vertical scaling factor s(k) of an iterated function system so that the obtained affine fractal interpolation function f(Delta) has the property that R(x)- d <= f(Delta)(x) <= R(x)+ D for all x is an element of I, where D and d are given positive constants and R(x)= mx+ c is a given linear function on I. As an example, we consider the case that the graph of R is the regression line that fits the given data points by least square method.