Newton's method on generalized Banach spaces

作者：Argyros Ioannis K^*; Behl Ramandeep; Motsa S S

来源：Journal of Complexity, 2016, 35: 16-28.

DOI：10.1016/j.jco.2015.12.002

• Generalized Banach space
• Newton's method
• Semilocal convergence
• Local convergence

We present a weaker convergence analysis of Newton's method than in Kantorovich and Akilov (1964), Meyer (1987), Potra and Ptak (1984), Rheinboldt (1978), Traub (1964) on a generalized Banach space setting to approximate a locally unique zero of an operator. This way we extend the applicability of Newton's method. Moreover, we obtain under the same conditions in the semilocal case weaker sufficient convergence criteria; tighter error bounds on the distances involved and an at least as precise information on the location of the solution. In the local case we obtain a larger radius of convergence and higher error estimates on the distances involved. Numerical examples illustrate the theoretical results.

• 出版日期2016-8