A unifying theorem for Newton's method on spaces with a convergence structure

作者：Argyros Ioannis K; Hilout Said^*

来源：Journal of Complexity, 2011, 27(1): 39-54.

DOI：10.1016/j.jco.2010.08.005

• Newton's method
• Banach space
• Convergence structure
• Fixed point
• Kantorovich hypothesis

We present a semilocal convergence theorem for Newton's method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1-3,5], Meyer (1984, 1987, 1992) [13-15]. Numerical examples are provided for solving equations in cases not covered before.

• 出版日期2011-2