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2017•International Journal of Theoretical and Applied MathematicsOpen access

A Method of the Best Approximation by Fractal Function

Yong-Suk Kang

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Abstract

We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.

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What this paper is about

We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.

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Available abstract

We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.

Key concepts: Fractal, Fractal derivative, Mathematics, Interpolation (computer graphics), Fractal dimension on networks, Function (biology), Multifractal system, Space (punctuation)

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