求解关联维数的快速算法研究

针对关联维数计算速度慢、耗时多和运算效率低的缺陷,本文从算法和结构两个方面研究了关联维数的快速求解方法,提出了区间阈值累加法和区间维值累加法.这两种算法通过对 · 表格的批处理填写以达到减少重复运算和提高计算效率的要求.文中详细地介绍了算法步骤,分析了算法的运算量,通过与标准算法和一般改进算法的比对,显示出本文提出算法的优越性.

Research of the Optimized Algorithm for the Calculation of Correlation Integrals

In order to solve the problem of slow speed,based on the canonical algorithm of calculation of the correlation integrals,this paper not only provides several improvements,but also puts forward two optimized algorithms.The algorithms are based on the region of embedded dimension and region of distance threshold.They are filled in table of (m_max is number of embedded dimension,r_maxis number of distance threshold) by batch methods giving up the one by one processing methods.In this paper,the theory and algorithm are narrated in detail.The performance of two optimal algorithms is compared with canonical algorithm and improvement method.The experimental result shows that optimal algorithms need least time to calculate the correlation dimension for same length time series with same number of distance threshold and embedded dimension since they have little redundant calculations and enhance the calculation efficiency obviously.