Simpson牛顿公式的一种改进  

Improvement of Simpson-Newton's iterative method

作　　者：李洋洋[1] 郭清伟[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2012年第6期853-856,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校省级自然科学研究资助项目(2010AJZR0884)

摘　　要：文章基于牛顿公理给出非线性方程求根的一种三阶方法,证明了该迭代格式三阶收敛到单根,计算效能高于其他同类迭代法;在方程根的重数m已知和未知的情形下,分别给出了该方法的改进公式,并指出了它们的收敛阶;最后给出数值试验并与其他方法进行比较,结果显示该方法非常有效,具有一定的理论价值和应用价值。A kind of third-order convergence method for solving roots of nonlinear equation is developed by using Newton axiom. It is proved that third-order convergence nears simple root and the computa- tional efficiency of the method is higher than that of other iterative methods. In the case of multiplici- ty rn of roots of equation heing known or unknown, the improved formula of the method and the order of convergence are given. Numerical tests are given and the results are compared with those of other iterative methods. It is shown that the proposed method is effective and it has some values in both theory and application.

关 键 词：牛顿迭代法 三阶收敛 效率指数 数值试验 

分 类 号：O242[理学—计算数学]