https://doi.org/10.1140/epjs/s11734-025-01998-x
Regular Article
Graph-directed fractal interpolation for multiple data sets with positivity and monotonicity preservation
1
Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Prasanthi Nilayam, 515134, Puttaparthi, Sri Sathya Sai District, Andhra Pradesh, India
2
Department of Mathematics, Indian Institute of Technology Madras, 600036, Chennai, Tamil Nadu, India
a
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Received:
17
March
2025
Accepted:
26
September
2025
Published online:
28
January
2026
Abstract
In this paper, we introduce a new interpolating scheme, graph-directed interpolation, for simultaneously interpolating multiple data sets using directed graphs. A 
-rational cubic graph-directed fractal interpolation function with a cubic numerator and a quadratic denominator, incorporating three shape parameters, has been developed based on the construction of a graph-directed iterated function system. This approach addresses the challenge of preserving positivity and monotonicity in scientific or experimental data sets. We establish a general framework for constructing graph-directed fractal interpolation functions and derive simple data-dependent conditions on scaling factors and shape parameters to ensure that the rational cubic graph-directed fractal interpolation function both modifies and preserves the positivity and monotonicity of the given data sets. Finally, we present visually appealing numerical illustrations to substantiate the effectiveness of our scheme.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
