Fractal interpolation functions (FIF) are defined as fixed points of contractive maps between spaces of continuous functions using iterated function systems. They are well suited to interpolate functions and data which display some sort of selfsimilarity. The graph of an FIF may have noninteger fractal dimension. There exist, however, also differentiable FIF. The authors describe a general way of constructing smooth FIF with the help of Hermite interpolating polynomials. A particular type of FIF associated with cubic splines is studied. Under suitable hypotheses bounds for the interpolation error for the function and its derivatives up to a certain order are obtained.
For the entire collection see [Zbl 1105.00005].