Majorizing sequences for Newton's method from initial value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Ezquerro, J. A.¹  Gonzalez, D.¹  Hernandez, M. A.¹ 

[1] Univ La Rioja, Dept Math & Computat, Logrono 26004, Spain

关键词: Newton's method;    Semilocal convergence;    Majorizing sequence;    Order of convergence;    Kantorovich's technique;    Bratu's equation;   

DOI  :  10.1016/j.cam.2011.11.012

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free