A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Alexandra Băicoianu, Cristina Maria Păcurar and Marius Păun
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Alexandra Băicoianu: Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Braşov 50, Iuliu Maniu Str., 500090 Braşov, Romania
Cristina Maria Păcurar: Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Braşov 50, Iuliu Maniu Str., 500090 Braşov, Romania
Marius Păun: Department of Forest Engineering, Forest Management Planing and Terrestrial Measurements, Faculty of Silviculture and Forest Engineering, Transilvania University of Braşov, 1 Şirul Beethoven, 500123 Braşov, Romania

Mathematics, 2021, vol. 9, issue 7, 1-12

Abstract: The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function (FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. P?curar.

Keywords: fractal interpolation function; non-affine FIFs; countable affine probabilistic scheme; countable affine deterministic scheme; countable non-linear probabilistic scheme; countable deterministic non-linear scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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