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Fractal interpolation over nonlinear partitions

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  • Massopust, Peter R.

Abstract

This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this context, perturbations of nonlinear partition functions are considered and sufficient conditions for the existence of a unique solution of the underlying fractal interpolation problem for some classes of function spaces are given.

Suggested Citation

  • Massopust, Peter R., 2022. "Fractal interpolation over nonlinear partitions," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007081
    DOI: 10.1016/j.chaos.2022.112503
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    References listed on IDEAS

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    1. Bandt, Christoph & Barnsley, Michael & Hegland, Markus & Vince, Andrew, 2016. "Old wine in fractal bottles I: Orthogonal expansions on self-referential spaces via fractal transformations," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 478-489.
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