摘要
对牛顿迭代公式进行改进,构造了新的迭代公式,并证明了其在单根附近至少具有二阶收敛性;以按揭贷款问题为算例,在MATLAB 7.1软件环境下编程,对简单迭代法、牛顿法、改进的算法进行了计算比较。结果表明,改进的算法不仅比简单迭代法收敛速度快、精度高,而且比牛顿法的精度高。
The Newton iterative formula was improved ,and a new iterative formula was constructed. It proved that the new iterative formula had at least second order convergence rate at single root. Taking mortgage loans for ex- ample,simple iterative method,Newton iterative method and improved method were carried on comparison with calculation in the MATLAB 7.1. The results showed that improved method converged more quickly than simple iterative method,and the method was higher in precision than simple iterative method and Newton method.
出处
《河北科技师范学院学报》
CAS
2011年第4期13-16,共4页
Journal of Hebei Normal University of Science & Technology
基金
秦皇岛市科技局项目(项目编号:201101A430)
关键词
牛顿迭代
非线性方程
收敛阶
按揭贷款
Newton iteration
nonlinear equations
order of convergence
mortgage loans
