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

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  • Viswanathan, P.

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.

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  • Viswanathan, P., 2022. "A revisit to smoothness preserving fractal perturbation of a bivariate function: Self-Referential counterpart to bicubic splines," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000960
    DOI: 10.1016/j.chaos.2022.111885
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    1. N. Vijender & A. K. B. Chand, 2021. "Shape Preserving Aspects Of Bivariate α-Fractal Function," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-13, November.
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    Cited by:

    1. Liu, Chiao-Wen & Luor, Dah-Chin, 2023. "Applications of fractal interpolants in kernel regression estimations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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