$$\mathbf {A}$$-Fractal Rational Functions and Their Positivity Aspects

S K Katiyar,A K B Chand

doi:10.1007/978-981-15-5411-7_16

$$\mathbf {A}$$-Fractal Rational Functions and Their Positivity Aspects

S K Katiyar, A K B Chand

https://doi.org/10.1007/978-981-15-5411-7_16

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Publication Date: Nov 26, 2020

Citations: 2

Affiliation: SRM Institute of Science and Technology, Indian Institute of Technology Madras

#Hidden Variable Fractal Interpolation Function #Coalescence Hidden Variable Fractal Interpolation + Show 8 more

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Abstract

Abstract Coalescence hidden variable fractal interpolation function (CHFIF) proves more versatile than classical interpolant and fractal interpolation function (FIF). Using rational functions and CHFIF, a general construction of $\mathbf {A}$-fractal rational functions is introduced for the first time in the literature. This construction of $\mathbf {A}$-fractal rational function also allows us to insert shape parameters for positivity-preserving univariate interpolation. The convergence analysis of the proposed scheme is established. With suitably chosen numerical examples and graphs, the effectiveness of the positivity-preserving interpolation scheme is illustrated.KeywordsIterated function systemFractalsFractal interpolation functionsHidden variable fractal interpolation functionConvergenceShape preservationPositivity

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