Majorizing functions and two-point Newton-type methods

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Abstract

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].

MSC

65G99
65K10
47H17
49M15

Keywords

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

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