| 牛顿方法的两个新格式 |
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| 引用本文： | 王霞,赵玲玲,李飞敏.牛顿方法的两个新格式[J].数学的实践与认识,2007,37(1):72-76. |
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| 作者姓名： | 王霞 赵玲玲 李飞敏 |
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| 作者单位： | 郑州轻工业学院信息与计算科学系,河南,郑州,450002 |
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| 基金项目： | 国家自然科学基金;郑州轻工业学院校科研和教改项目 |
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| 摘 要： | 给出牛顿迭代方法的两个新格式,S im pson牛顿方法和几何平均牛顿方法,证明了它们至少三次收敛到单根,线性收敛到重根.文末给出数值试验,且与其它已知牛顿法做了比较.结果表明收敛性方法具有较好的优越性,它们丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值.
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| 关 键 词： | 牛顿迭代法 收敛阶 数值试验 |
| 修稿时间： | 2005年12月12 |
Two New Schemes of Newton's Interation Method Squares Estimator is BLUE |
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| WANG Xia,ZHAO Ling-ling,LI Fei-min.Two New Schemes of Newton''''s Interation Method Squares Estimator is BLUE[J].Mathematics in Practice and Theory,2007,37(1):72-76. |
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| Authors: | WANG Xia ZHAO Ling-ling LI Fei-min |
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| Abstract: | Two new schemes of Newton′s method,which are Simpson Newton′s method and gemetric mean Newton′s method,are developed and their convergence properties are proved.They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton′s methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of non-linear equations and they are important in both theory and application. |
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| Keywords: | Newton′s iteration method convergence order numerical test |
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