Geodesic
Parameter identification of constrained data by a new class of rational fractal function
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 3, pp. 261-276.

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This paper sets a theoretical foundation for applications of fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with a quadratic denominator involving two shape parameters. The elements of the iterated function system (IFS) in each subinterval are identified befittingly so that the graph of the resulting $\mathcal{C}^1$-RCSFIF lies within a prescribed rectangle. These parameters include, in particular, conditions on the positivity of the $\mathcal{C}^1$-RCSFIF. The problem of visualization of constrained data is also addressed when the data is lying above a straight line, the proposed fractal curve is required to lie on the same side of the line. We illustrate our interpolation scheme with some numerical examples. 
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S. K. Katiyar; A. K. B. Chand; S. Jha. Parameter identification of constrained data by a new class of rational fractal function. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 3, pp. 261-276. http://geodesic.mathdoc.fr/item/SJVM_2021_24_3_a2/

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