用非精确的平行割线法求解奇异问题  

Inexact Parallel Secant Method at Singular Points

作　　者：杨月梅[1] 潘状元[2] 

机构地区：[1]哈尔滨金融学院基础部,黑龙江哈尔滨150030 [2]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《数学的实践与认识》2013年第6期240-245,共6页Mathematics in Practice and Theory

摘　　要：奇异方程经常出现在很多实际非线性问题中,如反应扩散系统等.因此,研究奇异非线性方程的求解具有十分重要的意义.平行割线法是一种经典的求解非线性方程的迭代方法,它收敛阶较高,计算量较少.但在解决实际问题时,一方面,抽象出的数学模型与实际问题总是存在着一定的偏差,另外,在数据的计算中难免存在着一定的计算误差,所以研究用非精确的平行割线法求解非线性奇异问题具有很重要的现实意义,使得求解奇异问题具有更高的实用性和可行性.采用在平行割线法的迭代公式中加入摄动项的方法,构造出新的加速迭代格式,证明了新的迭代格式的收敛性,给出了收敛速率,得到了误差估计.Singular equations are often arising in many practical nonlinear problems, such as in reaction-diffusion system etc. Therefore, It is of great significance to solve the singular nonlinear equations.Parallel secant method is a traditional iterative methods for solving the singular nonlinear equations. It has higher convergence order with less computation. Further- more, in practical problems, there exist deviations between the abstract mathematical models and practical problems. On the other hand, it is hard to avoid computational errors in data calculation. The research of solving singular nonlinear problems with inexact computational method is very important actually.In this paper, the new acceleration iterative schemes are constructed by adding perturbed term to the schemes, The convergence of the new acceleration iterative schemes is proved, the rate of convergence is given and the error is obtained. Keywords： inexact parallel secant method; singular problems; convergence; perturbation rate of convergence

关 键 词：非精确平行割线法 奇异问题 收敛性 摄动项 收敛速率 

分 类 号：O175[理学—数学]