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Multi-Dimensional Piece-Wise Self-Affine Fractal Interpolation Model In Tensor Form

Author

Listed:
  • TONG ZHANG

    (Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China)

  • JIANLIN LIU

    (Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China)

  • ZHUO ZHUANG

    (Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China)

Abstract

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine inR2orR3(Ris the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended fromR3toRn(nis an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model.This model uses a "mapping partial derivative" and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine inRn. Therefore, the result is very general. Moreover, the multi-dimensional piece-wise self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form.

Suggested Citation

  • Tong Zhang & Jianlin Liu & Zhuo Zhuang, 2006. "Multi-Dimensional Piece-Wise Self-Affine Fractal Interpolation Model In Tensor Form," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 287-293.
    • Handle: RePEc:wsi:acsxxx:v:09:y:2006:i:03:n:s0219525906000756
    DOI: 10.1142/S0219525906000756
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