Majorizing functions and two-point Newton-type methods

作者：Chen Jinhai^*; Argyros Ioannis K; Agarwal Ravi P

来源：Journal of Computational and Applied Mathematics, 2010, 234(5): 1473-1484.

DOI：10.1016/j.cam.2010.02.024

• Newton-type method
• Banach space
• Semi-local convergence
• Lipschitz condition
• Frechet derivative
• Majorizing sequences

The semi-local convergence of a Newton-type method used to solve nonlinear equations in a Banach space is studied. We also give, as two important applications, convergence analyses of two classes of two-point Newton-type methods including a method mentioned in [5] and the midpoint method studied in [1,2,12]. Recently, interest has been shown in such methods [3,4].

• 出版日期2010-7-1