对非线性常微分方程的参数估计和局部影响分析

›› 2014, Vol. 27 ›› Issue (1): 4-.

对非线性常微分方程的参数估计和局部影响分析

李慧慧,岳晓鹏

(西安电子科技大学理学院,陕西西安 710071)

出版日期:2014-01-15 发布日期:2014-01-12
作者简介:李慧慧(1990—),女,硕士研究生。研究方向:概率统计。E-mail:lihui88910@126.com
基金资助:
青年科学基金资助项目(11201360)

Parameter Estimation and Local Influence Analysis of Nolinear Ordinary Differential Equations Based on Case-deletion Model

LI Hui-Hui, YUE Xiao-Peng

(School of Science,Xidian University,Xi'an 710071,China)

Online:2014-01-15 Published:2014-01-12

摘要/Abstract

摘要：

通过引入B样条基函数,给出非线性常微分方程中未知参数的两步估计法。然后导出基于数据删除模型的广义Cook距离的计算公式,并说明该算法降低了计算量。最终利用FitzHugh-Nagumo方程的模拟实验,检验了该算法的有效性,同时与现有算法进行比较,分析证明了其优越性。

关键词: 非线性常微分方程;B样条基函数;数据删除模型;广义Cook距离

Abstract:

This paper presents a technique for estimating parameters of nonlinear ordinary differential equations by using B-spline Basis Functions.Case-deletion model is introduced to give formula of Generalized Cook's Distance.This algorithm can reduce computational load and improve the efficiency of computing.Effectiveness of the algorithm is checked by FitzHugh-Nagumo equation,and the superiority of the algorithm is demonstrated by a comparison with the algorithms available.

Key words: nonlinear ordinary differential equations;b spline basis function;case deletion model;cooks distance

中图分类号:

O175.1

李慧慧, 岳晓鹏. 对非线性常微分方程的参数估计和局部影响分析[J]. , 2014, 27(1): 4-.

LI Hui-Hui, YUE Xiao-Peng. Parameter Estimation and Local Influence Analysis of Nolinear Ordinary Differential Equations Based on Case-deletion Model[J]. , 2014, 27(1): 4-.