DOI: 10.5176/2251-1911_CMCGS53
Authors: Arya Kumar Bedabrata Chand
Abstract: Fractal interpolation functions provide a new insight to the natural deterministic approximation and modelling of complex phenomena. Cardinal natural cubic spline Coalescence Fractal Interpolantion Functions (CFIFs) are constructed through moments. Using tensor product of univariate bases of cardinal natural cubic CFIFs, the present paper proposes the construction of natural bicubic spline CFIFs over a rectangular grid R. Natural bicubic CFIFs are self-affine or non-self-affine in nature depending on the IFS parameters of these univariate natural cubic CFIFs. An upper bound of the difference between the natural bicubic CFIFs and an original function f ∈ C4[R], and their derivatives are deduced. The effects of hidden variables are demonstrated through suitably chosen examples.
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