Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators

Algorithms

Sergio Amat¹  Sonia Busquier¹  Concepción Berm﫞z¹  Ángel Alberto Magreñán² 

[1] Departamento de Matemática Aplicada y Estadística, Universidad de Cartagena, Cartagena 21833, Spain; E-Mails:;Escuela de Ingeniería, Universidad Internacional de La Rioja, C/Gran Vía 41, Logroño (La Rioja) 26005, Spain

关键词: Newton type methods;    third order;    semilocal convergence;    centered hypotheses;    divided differences;   

DOI  :  10.3390/a8030669

来源: mdpi

【 摘 要 】

This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented.

【 授权许可】

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