Volume 25, Issue 6
Convergence of Newton's Method for Systems of Equations with Constant Rank Derivatives

J. Comp. Math., 25 (2007), pp. 705-718.

Published online: 2007-12

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• Abstract

The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale's point estimate theorems as special cases, are obtained.

• Keywords

Newton's method, Overdetermined system, Lipschitz condition with $L$ average, Convergence, Rank.

49M15, 65F20, 65H10.

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@Article{JCM-25-705, author = {}, title = {Convergence of Newton's Method for Systems of Equations with Constant Rank Derivatives}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {6}, pages = {705--718}, abstract = {

The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale's point estimate theorems as special cases, are obtained.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8724.html} }
TY - JOUR T1 - Convergence of Newton's Method for Systems of Equations with Constant Rank Derivatives JO - Journal of Computational Mathematics VL - 6 SP - 705 EP - 718 PY - 2007 DA - 2007/12 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8724.html KW - Newton's method, Overdetermined system, Lipschitz condition with $L$ average, Convergence, Rank. AB -

The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale's point estimate theorems as special cases, are obtained.

Xiubin Xu & Chong Li. (1970). Convergence of Newton's Method for Systems of Equations with Constant Rank Derivatives. Journal of Computational Mathematics. 25 (6). 705-718. doi:
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