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A general construction of fractal interpolation functions on grids of n

Published online by Cambridge University Press:  01 August 2007

P. BOUBOULIS  and
L. DALLA
P. BOUBOULIS
Affiliation:
Department of Informatics and Telecommunications, University of Athens, Panepistimiopolis 157 84, Athens, Greece email: bouboulis@di.uoa.gr
L. DALLA
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece email: ldalla@math.uoa.gr
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Abstract

We generalise the notion of fractal interpolation functions (FIFs) to allow data sets of the form where I=[0,1]n. We introduce recurrent iterated function systems whose attractors G are graphs of continuous functions f:I→, which interpolate the data. We show that the proposed constructions generalise the previously existed ones on . We also present some relations between FIFs and the Laplace partial differential equation with Dirichlet boundary conditions. Finally, the fractal dimensions of a class of FIFs are derived and some methods for the construction of functions of class Cp using recurrent iterated function systems are presented.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 4 , August 2007 , pp. 449 - 476
Copyright
Copyright © Cambridge University Press 2007

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