Graph-directed random fractal interpolation function
DOI:
https://doi.org/10.24193/subbmath.2021.2.01Keywords:
fractal interpolation function, iterated function system, random fractal interpolation functionAbstract
Barnsley introduced in [1] the notion of fractal interpola-tion function (FIF). He said that a fractal function is a (FIF) if it possess some interpolation properties. It has the advantage that it canbe also combine with the classical methods or real data interpolation. Hutchinson and Ruschendorf [7] gave the stochastic version of fractalinterpolation function. In order to obtain fractal interpolation functionswith more flexibility Wang and Yu [9] use instead of a constant scalingparameter a variable vertical scaling factor. Also the notion of fractal in-terpolation can be generalized to the graph-directed case introduced byDeniz and ̈Ozdemir in [5]. In this paper we study the case of a stochasticfractal interpolation function with graph-directed fractal function.References
M.F. Barnsley:Fractal functions and interpolation, Constructive Approxima-tion,2(1986), 303-329
M.F. Barnsley, S. Demko:Iterated function systems and the global constructionof fractals,Pro. Roy. Soc. London,A399(1985), 243-275
M.F. Barnsley:Fractals Everywhere, Academic Press, 1993.
A.K.B.Chand, G.P.Kapoor,Generalized cubic spline interpolation function,SIAM J. Numer. Anal.44(2), 655-676(2006)
A. Deniz, Y. ̈Ozdemir,Grapd-Directed Fractal Interpolation Functions, Turk.J. Math.,41(2017), 829-840.
Edgar, G., Measure, Topology and Fractal Geometry, Springer, New York,2008.
J.E.Hutchinson, L.R ̈uschendorf:Selfsimilar Fractals and Selfsimilar RandomFractals,Progress in Probability,46, (2000), 109-123.
M.A. Nevascu ́es, M.V. Sebasti ́an:Generalization of Hermite functions by frac-tal interpolation,J. Approx. Theory131(1), 2004, 19-29
H.Y. Wang, J.S. Yu:Fractal interpolation functions with variable parametersand their analytical properties,J. Approx. Theory175, 2013, 1-18