Majorizing sequences for Newton's method from initial value problems

Abstract:

The most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton's method in Banach spaces is relaxed in this paper, providing we can guarantee the semilocal convergence in situations that Kantorovich cannot. To achieve this, we use Kantorovich's technique based on majorizing sequences, but our majorizing sequences are obtained differently, by solving initial value problems. © 2011 Elsevier B.V. All rights reserved.

Año de publicación:

2012

Keywords:

• Newton's method
• Majorizing sequence
• Kantorovich's technique
• Bratu's equation
• Order of convergence
• semilocal convergence

Fuente:

scopus