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| Determining the Local Singularity Exponents and Spectrum of the Fractal Function |
| Wang Zhao-rui①; Lü Shan-wei①; Nakamura Taketsune② |
| ①School of Electronic and Information Engineering, Beihang University, Beijing 100083, China; ②Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan |
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Abstract Traditional partition function-based multifractal formalism provides only global estimates of singularity exponents, no local information is offered. However, it is more important to recover the local singularity. A novel algorithm for determining the local singularity exponents is proposed, which provides the local scaling information of interest, whilst a singularity-spectrum-like histogram is constructed to describe the global statistical distribution of the local singularity strengths. The validity is verified by numerical experiment.
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Received: 09 August 2006
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2008, Vol. 30 
