映射动力系统一维流形并行计算方法

A parallel algorithm for approximating 1-D manifold of maps

为了寻找一种映射系统流形计算的快速算法,提出一种计算映射动力系统双曲不动点一维流形的并行快速算法。该算法首先以区域迭代的方法为基础,对局部流形进行分割,然后运用了曲率约束和距离控制条件进行插值运算,在单个区间上独立计算映射值,独立检查精度,真正实现计算的并行化控制流形的增长;其次从理论上证明了流形并行计算的可能性,并给出了并行计算的实现方法;最后的实验数据和仿真结果表明:该方法既保证计算的速度又提高了计算的精度。

A fast parallel algorithm for computing one-dimensional manifold of a hyperbolic fixed point of a map was presented.With the new algorithm,field iteration was taken as a basic idea.The local manifold was subdivided,the curvature constraint and distance control condition were used to implement interation computation. Independently computing map values and checking accuracy were done in each interval to realize parallel computations and control the growth of manifold.The feasibility of manifold parallel computation was proved theoretically.Simulations and test data indicated that the proposed algorithm has a faster computing sped and a better accuracy.