On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator
Dynamical Systems
2020-10-13 v1 Numerical Analysis
Functional Analysis
Numerical Analysis
Abstract
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal functions simultaneously interpolating and approximating a prescribed bivariate continuous function. Some elementary properties of the associated nonlinear (not necessarily linear) fractal operator are established, thereby initiating the interaction of the notion of fractal interpolation with the theory of nonlinear operators.
Keywords
Cite
@article{arxiv.2010.05467,
title = {On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator},
author = {K. K. Pandey and P. Viswanathan},
journal= {arXiv preprint arXiv:2010.05467},
year = {2020}
}
Comments
21 Pages. Submitted to a Journal for Possible Publication in July 2020