Fractal functions and interpolation
type: Item
instance of: scholarly article
title: Fractal functions and interpolation
zbMATH Open document ID: 0606.41005
DOI: 10.1007/BF01893434
published in: Constructive Approximation
publication date: 1986-01-01T00:00:00Z
review text: Consider a set of data points \(\{x_ i,y_ i)\in I\times R:i=0,...,N\}\), where \(I=[x_ 0,x_ N]\subseteq R\). The author considers continuous functions f:I\(\to R\) which interpolate the given data, i.e. \(f(x_ i)=y_ i\), and such that there exist a compact subset \(K=I\times [a,b]\subseteq R^ 2\) and continuous functions \(w_ n:K\to K\) such that the graph G of f is the unique closed subset of K satisfying \(G=\cup^{N}_{n=1}w_ n(G)\). Such a function f is called a fractal interpolation function. It can occur that the Hausdorff-Besicovitch dimension of G is noninteger, usually for functions f which are Hölder but not differentiable. (For the theory of fractal sets see e.g. \textit{K. J. Falconer}, The geometry of fractal sets (1985; Zbl 0587.28004.) The fractal interpolation can be used to approximate wilder functions such as temperature in flames, electroencephalograph pen traces, etc. The author also discusses the associated coding theory and measure theory and evaluates explicitly moment integrals for a wide class of fractial interpolation functions.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 94A24
zbMATH DE Number: 3979666
zbMATH Keywords: fractal interpolation
author: Michael F. Barnsley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3979666