| A new method of approximating experimental data —— fractalinterpolation is introduced. The dimension of fractal interpolation (FIF) and its expression with wavelets series are discussed. Firstly, the appearance, development and main theory of fractal theory are proposed. Secondly, the fruits of fractal interpolation about IFS's attractor and box dimension and stability are summarized. On this base, the properties of FIF's Vf,δ are retained, the degree of Vf,δ are estimated. Then thedimension theorem of FIF is proved, but the minimum of boxes are replaced by Vf,δ.A new way to prove or calculate dimension is gained.Next, the one dimension FIF's expression with wavelet series is gained. The remainder of series is estimated , it goes to the zero. The expression of FIF under any accuracy is gained. At last, when the maximum of estimation can arrived is derived. Thus a useful expression of FIF is obtained. A new method is exploited for studying theory of FIF and practical calculation.
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