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Multi-dimensional self-affine fractal interpolation model in tensor form

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Abstract

Iterated Function System (IFS) models have been explored to represent discrete sequences where the attractor of an IFS is self-affine either in R 2 or R 3 (R is the set of real numbers). In this paper, the self-affine IFS model is extended from R 3 to R n (n is an integer and greater than 3), which is called the multi-dimensional self-affine fractal interpolation model. This new model is presented by introducing the defined parameter “mapping partial derivative”. A constrained inverse algorithm is given for the identification of the model parameters. The values of this new model depend continuously on all of the variables. That is, the function is determined by the coefficients of the possibly multi-dimensional affine maps. So the new model is presented as much more general and significant. Moreover, the multi-dimensional self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form.

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Author notes

  1. Tong Zhang

    Present address: Solid Mechanics Research Center, Beijing University of Aero & Astro, Beijing, 100083, China

Authors and Affiliations

  1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China

    Tong Zhang, Jian Lin Liu & Zhuo Zhuang

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  1. Tong Zhang
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  2. Jian Lin Liu
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  3. Zhuo Zhuang
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Correspondence to Tong Zhang.

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Zhang, T., Liu, J.L. & Zhuang, Z. Multi-dimensional self-affine fractal interpolation model in tensor form. Nonlinear Dyn 52, 83–87 (2008). https://doi.org/10.1007/s11071-007-9259-5

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  • DOI: https://doi.org/10.1007/s11071-007-9259-5

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