Error analysis for bivariate fractal interpolation functions generated by 3-D perturbed iterated function systems

Abstract

Based on a determined 3-D iterated function system (IFS), we introduce a perturbed IFS in R3. The attractor of the perturbed IFS is the graph of a bivariate fractal interpolation function (FIF) that interpolates arbitrarily given data on rectangular grids of R2. We consider the error problem between the FIF generated by the perturbed IFS and the FIF generated by the original IFS. An explicit relation of the difference between the two bivariate FIFs is presented. Furthermore, we investigate the error of moment integrals of the two FIFs. An upper bound estimate for the error of moments is obtained.