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MULTI-DIMENSIONAL PIECE-WISE SELF-AFFINE FRACTAL INTERPOLATION MODEL IN TENSOR FORM

TONG ZHANG

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

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JIANLIN LIU

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

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ZHUO ZHUANG

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

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https://doi.org/10.1142/S0219525906000756Cited by:3 (Source: Crossref)

Abstract

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R² or R³ (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R³ to Rⁿ (n is 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 in Rⁿ. 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.

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