# On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator

Source: [On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator](<https://www.sota2.com/research/paper/68fa57711e209131ce9a550b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T14:43:29.035Z

Authors: K.K. Pandey, P. Viswanathan

Published: 2020-10-12T05:55:42.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2010.05467>)

[PDF](<https://arxiv.org/pdf/2010.05467.pdf>)