摘要
基于Thiele连分式,重新建立了求解非线性方程的经典的Newton迭代公式.为了避免求导数运算,采用差商可以近似代替导数的办法,得到Newton迭代方法的几个变体并给出了其收敛的阶数.最后,数值实例证实了这些迭代格式是有效的.
Based on Thiele＇s continued fraction, the Newton＇s iterative formula is reconstructed for solving nonlinear equations in this paper. In order to avoid computing functional derivatives, several variants of Newton＇s mehtod are presented by means of divided differences and their orders of convergence are given. At last numerical examples are computed to verify that these iterative schemes are effective.
出处
《大学数学》
2009年第3期35-40,共6页
College Mathematics
基金
安徽省高校青年教师科研资助项目(2008jq1158)
蚌埠学院自然科学研究项目(BBXY2007-203A)
蚌埠学院教育教学研究项目(YJJY0822)
关键词
连分式
NEWTON迭代
差商
收敛阶数
continued fraction
Newton＇s method
divided difference
order of convergence
