Numerical Properties of Different Root-Finding Algorithms Obtained for Approximating Continuous Newton’s Method

Algorithms

José M. Gutiérrez¹  Alicia Cordero¹  Juan R. Torregrosa¹ 

[1] Department of Mathematics and Computer Sciences, University of La Rioja, Logroño 26004, Spain; E-Mail

关键词: continuous Newton’s method;    Newton’s method;    nonlinear equations;    iterative methods;   

DOI  :  10.3390/a8041210

来源: mdpi

【 摘 要 】

This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of convergence is particularly considered. We have analyzed both the cases of a constant and non-constant step size in the procedure of integration. We show that working with a non-constant step, the well-known Chebyshev-Halley family of iterative methods for solving nonlinear scalar equations is obtained.

【 授权许可】

CC BY   
© 2015 by the author; licensee MDPI, Basel, Switzerland.