Research on Optimal Interpolation Times of Nonlinear Time-Series Using Metric Entropy and Fractal Interpolation

In the field of geoscience and atmospheric science, raw data should be interpolated by appropriate times due to the temporal and spatial resolution limitation or the length of initial data at the given observation time for the follow-up process. But this type of data have universal and special nonlinear characteristics, such as chaotic and fractal feature, these nonlinear time series are sensitive to initial condition when applied to model, so it means that the optimal approximation by interpolation to the raw data is required, there will be existing an optimal interpolation times to the data but not arbitrary times. In this paper, we propose a new approach by applying fractal interpolation and Metric Entropy to retrieve the optimal interpolation times. it´s found that higher order nonlinear fractal interpolation function can determine the optimal interpolation times for raw data without changing its initial structure and nonlinear characteristics under the constraining of Metric Entropy. This conclusion will be significant and used abroad in information science and physical science and so on.