A revisit to smoothness preserving fractal perturbation of a bivariate function: Self-Referential counterpart to bicubic splines

P. Viswanathan

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

Abstract: Construction of fractal interpolation surfaces has recently been considered in the standpoint of a parameterized class of fractal (self-referential) functions corresponding to a given bivariate continuous function. In this paper, we describe a procedure so that the elements in this parameterized class preserve smoothness (C(2,2)-regularity) of the original bivariate function defined on a rectangle. As a consequence, we generalize the bicubic spline by means of a two-parameter family of fractal functions, which we call bicubic fractal splines. Under certain hypotheses, upper bounds for the interpolation error for the bicubic fractal spline and its derivatives are obtained. A detailed exposition of C(2,2)-regular self-referential functions is provided not only as a prelude to the bicubic fractal splines, but also to elucidate the study of smoothness preserving bivariate self-referential functions appeared recently in the fractal literature.

Keywords: Fractal interpolation; Splines; Bicubic splines; Bivariate alpha-fractal function; Approximation error (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000960

DOI: 10.1016/j.chaos.2022.111885

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