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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 formwhere 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.

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

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