东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2005, Vol. 26 ›› Issue (4): 242-244.DOI: -

• 论著 • 上一篇    下一篇

非线性代数映射问题分支值的一种高精度快速算法

侯祥林;韩旭   

  1. 东北大学理学院;沈阳工业大学建筑工程学院 辽宁沈阳　110004
  • 收稿日期:2013-06-24 修回日期:2013-06-24 出版日期:2005-04-15 发布日期:2013-06-24
  • 通讯作者: Hou, X.-L.
  • 作者简介:-
  • 基金资助:
    辽宁省博士启动基金资助项目(2001102017)·

Fast high-precision algorithm for ramification value of nonlinear algebraic mapping problems

Hou, Xiang-Lin (1); Han, Xu (2)   

  1. (1) Sch. of Sci., Northeastern Univ., Shenyang 110004, China; (2) Sch. of Arch. Eng., Shenyang Univ. of Technol., Shenyang 110023, China
  • Received:2013-06-24 Revised:2013-06-24 Online:2005-04-15 Published:2013-06-24
  • Contact: Hou, X.-L.
  • About author:-
  • Supported by:
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摘要： 研究了非线性代数映射动力系统分支值确定问题,提出二分缩减确定分支值的高精度新算法·克服了步长增量法由于细化步长造成计算时间较长的问题,解决了分支值优化算法由于目标函数本身构成产生较大计算误差的弱点·通过对典型的Logistic映射算例的倍周期分支值编程分析计算,给出误差限为10-10精确的分支值·这种算法既节省计算时间又具有高的计算精度·该方法为非线性系统与混沌特性研究提供了条件·

关键词: 代数迭代系统, Logistic映射, 分支值, 二分缩减算法, 混沌

Abstract: The ramification values of nonlinear algebraic mapping dynamic system are studied, and a novel high precision algorithm of dimidiate reducing ramification values is proposed. Thus, the longer computing time spent for the step redistribution in the step-increment algorithm can be shortened, and the relatively low computing accuracy of optimal algorithm for ramification values, which are due to the errors of the objective function itself, can be improved further. A logistic mapping problem is computed typically via the programming and a number of ramifications values are obtained within the accuracy of 10-10. Compared with other existing algorithms, the method proposed is faster in computing speed and higher in precision, and will provide a reference for nonlinear problem and chaos studying.

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