caa a22 4500 606166521 CHVBK 20210128100658.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10440-014-9882-3 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9882-3 A $\mathcal{C}^{1}$ -Rational Cubic Fractal Interpolation Function: Convergence and Associated Parameter Identification Problem [Elektronische Daten] [P. Viswanathan, A. Chand] This paper introduces a rational Fractal Interpolation Function (FIF), in the sense that it is obtained using a rational cubic spline transformation involving two shape parameters, and investigates its applicability in some constrained interpolation problems. We identify suitable values for the parameters of the corresponding Iterated Function System (IFS) so that it generates positive rational FIFs for a given set of positive data. Further, the problem of identifying the rational IFS parameters so as to ensure that its attractor (graph of the corresponding rational FIF) lies in a specified rectangle is also addressed. With the assumption that the data defining function is continuously differentiable, an upper bound for the interpolation error (with respect to the uniform norm) for the rational FIF is obtained. As a consequence, the uniform convergence of the rational FIF to the original function as the norm of the partition tends to zero is proven. Springer Science+Business Media Dordrecht, 2014 Fractals nationallicence Iterated function systems nationallicence Rational fractal functions nationallicence Convergence nationallicence Positivity nationallicence Parameter identification nationallicence Viswanathan P. Department of Mathematics, Indian Institute of Technology Madras, 600036, Chennai, India aut Chand A. Department of Mathematics, Indian Institute of Technology Madras, 600036, Chennai, India aut Acta Applicandae Mathematicae Springer Netherlands 136/1(2015-04-01), 19-41 0167-8019 136:1<19 2015 136 10440 https://doi.org/10.1007/s10440-014-9882-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9882-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Viswanathan P. Department of Mathematics, Indian Institute of Technology Madras, 600036, Chennai, India aut NATIONALLICENCE 700 1- Chand A. Department of Mathematics, Indian Institute of Technology Madras, 600036, Chennai, India aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 136/1(2015-04-01), 19-41 0167-8019 136:1<19 2015 136 10440