| 基于连分式重新推导的Newton迭代公式及其变体 |
| |
| 引用本文： | 董毅,李声锋.基于连分式重新推导的Newton迭代公式及其变体[J].大学数学,2009,25(3). |
| |
| 作者姓名： | 董毅 李声锋 |
| |
| 作者单位： | 蚌埠学院,理学系,安徽,蚌埠,233000 |
| |
| 基金项目： | 安徽省高校青年教师科研资助项目，蚌埠学院自然科学研究项目，蚌埠学院教育教学研究项目 |
| |
| 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.
|
| 关 键 词： | 连分式 Newton迭代 差商 收敛阶数 |
The Rededuced Newton's Iterative Formula Based on Continued Fraction and Its Variants |
| |
| DONG Yi,LI Sheng-feng.The Rededuced Newton's Iterative Formula Based on Continued Fraction and Its Variants[J].College Mathematics,2009,25(3). |
| |
| Authors: | DONG Yi LI Sheng-feng |
| |
| Institution: | Department of Science;Bengbu College;Bengbu;Anhui 233000;China |
| |
| Abstract: | 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. |
| |
| Keywords: | continued fraction Newton's method divided difference order of convergence |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
