On the R-order of convergence of Newton's method under mild differentiability conditions

• Published in: Journal of computational and applied mathematics Vol. 197; no. 1; pp. 53 - 61
• Main Authors: Ezquerro, J.A., Hernández, M.A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-12-2006; Elsevier
• Subjects: A priori error bounds; Exact sciences and technology; Mathematical analysis; Mathematics; Newton's method; Nonlinear equations in Banach spaces; Nonlinear integral equation; Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Operator theory; R-order of convergence; Sciences and techniques of general use; Semilocal convergence theorem; Nonlinear integral equation; Nonlinear equations in Banach spaces; Newton's method; Semilocal convergence theorem; R-order of convergence; A priori error bounds; 47H17; 65J15; Non linear equation; Numerical analysis; Nonlinear equations in Banach spaces; Newton's method; Semilocal convergence theorem; R-order of convergence; A priori error bounds; Nonlinear integral equation; Applied mathematics; 47H17; 65J15; Integral equation; Banach space; Newton method; Kantorovich condition
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2005.10.023

A new technique is used instead of the classical majorant principle to analyze the
R-order of convergence of the Newton process when more general conditions than the Kantorovich ones are considered.