After notes on Chebyshev’s iterative method

Applied Mathematics and Nonlinear Sciences

Amat S.¹  Busquier S.¹ 

[1] Department of Applied Mathematics and Statistics, Technical University of Cartagena, Cartagena, Spain;

关键词: nonlinear equations;    chebyshev’s iterative method;    geometric interpretation;    global convergence;    dynamics;    applications;    65j15;   

DOI  :  10.21042/AMNS.2017.1.00001

来源: DOAJ

【 摘 要 】

This paper is a small review of Chebyshev’s method. The geometric interpretation as a generalization of Newton’s method is derived. Using this interpretation its global convergence is proved. Some dynamical properties are studied. As a higher order method, they are more complicated than in Newton’s method. Finally, some applications are revisited pointing out the advantages of Chebyshev’s method with respect Newton’s method.

【 授权许可】

Unknown