Efficient implementation of the Gaussian kernel algorithm in estimating invariants and noise level from noisy time series data

We describe an efficient algorithm which computes the Gaussian kernel corre lation integral from noisy time series: this is subsequently used to estima te the underlying correlation dimension and noise level in the noisy data. The algorithm first decomposes the integral core into two separate calculat ions, reducing computing time from O(N-2 x N-b) to O(N-2 +N-b(2)). With oth er further improvements, this algorithm can speed up the calculation of the Gaussian kernel correlation integral by a factor of gamma similar to(2-10) N-b. We use typical examples to demonstrate the use of the improved Gaussia n kernel algorithm.