Fractal Interpolation Functions on the Stability of Vertical Scale Factor

Abstract: Fractal interpolation is a new interpolation method, the corresponding vertical scale factor determines the shape of fractal interpolation functions and features. Therefore, choosing the appropriate vertical scale factor, can fit the real rough curve precisely. This paper primarily studies the change of the fractal interpolation curve when giving a small perturbation on vertical scale factor, the fractal interpolation curve produces change. When the vertical scale factor has a small change, in order to satisfy the continuity condition, its iteration function must have the corresponding change, so, give the corresponding iterated function system. Next, this paper discusses the changes of fractal interpolation functions when the vertical scale factor perturbate and give the error estimate.