Investigation of Fast Algorithm for Correlation Integral Method

Two fast algorithms for correlation integral (i.e. CI) method are presented based on our investigative result that the number of the correlated pairs in phase space is equal to the summation of the number of the pairs in each set and between distinct pairs of sets when the phase space is divided into some sets of points. Uniform computational analysis allows a clear comparison of the two algorithms, and indicates they are both able to improve the efficiency of the correlation integral method remarkably. The first decreases only the computational complexity of partial CI; the second is powerful since it reduces that of all CI except the first one. Therefore, the second is in particular suitable for fast processing of long time series. They will motivate the application of correlation integral method in the relevant fields. More generally, the computational framework can be used in similar problems involving long-range interactions