Affine zipper fractal interpolation functions

This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identifie...

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Bibliographic Details
Published inBIT Vol. 60; no. 2; pp. 319 - 344
Main Authors Chand, A. K. B., Vijender, N., Viswanathan, P., Tetenov, A. V.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2020
Springer Nature B.V
Subjects
Computational Mathematics and Numerical Analysis
Fractals
Interpolation
Mathematics
Mathematics and Statistics
Numeric Computing
Scaling factors
Box counting dimension
28A80
Affine zipper fractal function
Integral equation
Zipper
46N20
41A05
Fractal interpolation function
26A18
41A29
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Summary:This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identified so that the graph of the corresponding affine zipper fractal interpolation function can be inscribed within a prescribed rectangle. Convergence analysis of the proposed affine zipper fractal interpolant is carried out. It is observed that for a fixed choice of discrete scaling factors, the box counting dimension of the graph of an affine zipper fractal interpolant is independent of the choice of a signature. Several examples of affine zipper fractal interpolants are presented to supplement our theory.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-019-00774-3