动力系统精细算法的逼近机理与误差分析

The Approximate Mechanism and Error Analysis of Precise Computation for Dynamics System

发现以下3者的协同作用是实现精细算法高精度、高效率的内在机制和根本原因：指数矩阵eHx的Maclaurin组数展开式绝对收敛；2）初始Maclaurin级数展开式中的有效展开项总数能够通过递推算法以指数方式扩展；3）新增有效展开项的系数能够通过递推算法以指数或拟指数方式逼近其真值。除此之外，还研究了初始Maclaurin级数展开式中的保留项数和选用的递推阶数等因素对精细算法逼近过程和逼近精度的影响，发现在多数情况下，适当增加保留项数比单纯增加递推阶数更有利于逼近精度的提高和逼近过程的加速实现。

The present paper discovers that the inherent mechanism and basic cause of realizing the high approximate precision and computational efficiency by the precision computation method for dynamics system lies in the cooperation of the following three factors: the expansion of exponential matrix eHx in Maclaurin series is absolutely convergent 2)the active expansion item of exponential matrix eHx in Maclaurin series increase exponentially as recurrent course. 3)the coefficients of newly adding active expansion items will approximate their actual values exponentially or quasi-exponentially as recurrent course. Besides, the effects for original reserved item M or recursion order N are dis- cussed, and the following rule is discovered that the approximate error of the precision computation method decrease ex- ponentially as increasing of reserved item M or recursion order N.