Modified Newton's method for systems of nonlinear equations with singular Jacobian

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:224

Article

Hueso, Jose L.¹  Martinez, Eulalia¹  Torregrosa, Juan R.¹ 

[1] Univ Politecn Valencia, Inst Matemat Pura & Aplicada, Inst Matemat Multidisciplinar, Valencia 46022, Spain

关键词: Newton's method;    Jacobian matrix;    Order of convergence;    Fixed point function;   

DOI  :  10.1016/j.cam.2008.04.013

来源: Elsevier

【 摘 要 】

It is well known that Newton's method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification of this method for nonlinear systems whose Jacobian matrix is singular. We prove, under certain conditions, that this modified Newton's method has quadratic convergence. Moreover, different numerical tests confirm the theoretical results and allow us to compare this variant with the classical Newton's method. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free