Article ID Journal Published Year Pages File Type
4639785 Journal of Computational and Applied Mathematics 2012 13 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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