改进的牛顿预测—–校正格式

被引：8

作者：

吕巍 ^{[1
]}

隋瑞瑞 ^{[1
]}

冯恩民 ^{[2
]}

机构：

[1] 上海大学数学系

[2] 大连理工大学数学科学学院

来源：

控制理论与应用 | 2015年 / 32卷 / 12期

关键词：

牛顿算法; 预测–校正格式; 非线性方程; 迭代方法;

D O I：

暂无

中图分类号：

O241.7 [非线性代数方程和超越方程的数值解法];

学科分类号：

070102 [计算数学];

摘要：

在数值分析领域中,牛顿算法由于其形式的简单性及快速的收敛性而被广泛地应用于求解非线性方程问题.受一类求解方程的预测–校正技术的启示,本文针对求解非线性方程单根的问题提出了一种牛顿预测–校正格式,并将其推广到多维向量值函数情况.为此,首先用图描述了这种新的预测–校正格式并导出了其收敛阶.这种新格式每步迭代仅需计算一次函数值和一次导函数值.然后,经过测试函数的检验,并与牛顿算法及其他高阶算法(1+√2阶、3阶、4阶、5阶、6阶)比较,表明新算法具有较快的收敛性.最后,将这种新格式推广到多维向量值函数,采用泰勒公式证明了其收敛性,并给出了一个二维算例来验证其收敛的有效性.

引用

页码：1620 / 1626

页数：7

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