Enhanced box and prism assisted algorithms for computing the correlation dimension

Box-assisted and prism-assisted algorithms are among the most popular algorithms for the computation of the correlation dimension. However, the box size is usually determined by authors just through rough estimates or even by trial and error. In this paper, an explicit criterion for the selection of the optimal box size in box-assisted algorithms is presented. When used in conjunction with even the simplest box-assisted algorithm, the computation time needed to estimate the correlation integral is drastically reduced. These reductions range from a factor of 10 to factors larger than 1000, depending on the complexity of the attractor and/or the length of the dataset.