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Numerical Analysis and Applications

2021 year, number 2

Generalized bivariate Hermite fractal interpolation function

Sangita Jha1, A.K.B. Chand1, M.A. Navascues2
1Indian Institute of Technology Madras, Chennai, India
2Universidad de Zaragoza, Zaragoza, Spain
Keywords: fractals, fractal interpolation, hermite interpolation, fractal surface, convergence


Fractal interpolation provides an efficient way to describe the smooth or non-smooth structure associated with nature and scientific data. The aim of this paper is to introduce a bivariate Hermite fractal interpolation formula which generalizes the classical Hermite interpolation formula for two variables. It is shown here that the proposed Hermite fractal interpolation function and its derivatives of all orders are good approximations of the original function even if the partial derivatives of the original functions are non-smooth in nature.