Interval Newton method for solving nonlinear equations with roots

Computer Engineering and Applications ›› 2012, Vol. 48 ›› Issue (31): 40-42.

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Interval Newton method for solving nonlinear equations with roots

ZHANG Haidi, CAO Dexin

School of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Online:2012-11-01 Published:2012-10-30

求解非线性方程重根的区间牛顿法

张海蒂，曹德欣

中国矿业大学理学院，江苏徐州 221116

Abstract

Abstract: Nonlinear equations for solving the roots are discussed, for the interval Newton method is no longer applicable and the convergence of the improved interval Newton method is so slow, by introducing a correlative equation, a new improved interval Newton method for solving the roots of nonlinear equations is established. Its local quadratic convergence property is proved, numerical examples are given. That the new method has faster convergence speed than the improved interval Newton method is verified, and it is effective and reliable.

Key words: nonlinear equations, interval algorithm, interval Newton method

摘要： 讨论了求解非线性方程重根问题，针对此时Moore区间牛顿法不再适用，以及Hansen改进的区间牛顿法收敛速度慢的情况，通过引入原方程的一种相关方程，建立了求解非线性方程重根的区间牛顿法；证明了其局部平方收敛的性质，给出了数值算例。验证了新算法比Hansen改进的区间牛顿法具有更快的收敛速度，且算法是有效和可靠的。

关键词: 非线性方程, 区间算法, 区间牛顿法

ZHANG Haidi, CAO Dexin. Interval Newton method for solving nonlinear equations with roots[J]. Computer Engineering and Applications, 2012, 48(31): 40-42.

张海蒂，曹德欣. 求解非线性方程重根的区间牛顿法[J]. 计算机工程与应用, 2012, 48(31): 40-42.

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Interval Newton method for solving nonlinear equations with roots

求解非线性方程重根的区间牛顿法

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