A modified Newton method for rootfinding with cubic convergence

By Herbert H. H. Homeier. 2003

120 citations recorded by the source corpus.

We consider a modification of the Newton method for finding a zero of a univariate function. The case of multiple roots is not treated. It is proven that the modification converges cubically. Per iteration it requires one evaluation of the function and two evaluations of its derivative. Thus, the modification is suitable if the calculation of the derivative has a similar or lower cost than that of the function itself. Classes of such functions are sketched and a numerical example is given.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/71da194bf07b383fba03b0551cd8668bf78b2ee0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. M. A. Hernández
2. José Antonio Ezquerro
3. Xintao Ye
4. Chong Li

In Computational Theory and Mathematics

1. M. A. Hernández
2. José Antonio Ezquerro
3. Dharmendra Kumar Gupta
4. Pradip Kumar Parida

In Numerical Analysis

1. M. A. Hernández
2. José Antonio Ezquerro
3. Xintao Ye
4. Chong Li
5. Dharmendra Kumar Gupta
6. Pradip Kumar Parida

Citations in the corpus

• New iterations of R-order four with reduced computational cost (2009, methodology): “For example, in [6, 8 , 9], we can see Newtontype methods for rootfinding with cubic convergence.”