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

Authors:
Hong-Yong Wang;Shou-Zhi Yang;Xiu-Juan Li
Affiliations:
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, PR China;Department of Mathematics, Shantou University, Shantou 515063, PR China;College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

Based on a determined 3-D iterated function system (IFS), we introduce a perturbed IFS in R^3. 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 R^2. 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.