Affine zipper fractal interpolation functions

A. K. B. Chand, N. Vijender, P. Viswanathan, Андрей Викторович Тетенов

Research output: Contribution to journalArticle

Abstract

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
Original languageEnglish
Pages (from-to)319-344
Number of pages26
JournalBIT Numerical Mathematics
Volume60
Issue number2
Early online date6 Sep 2019
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Affine zipper fractal function
  • Box counting dimension
  • Fractal interpolation function
  • Integral equation
  • Zipper

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