TY - JOUR
T1 - Convergence of Newton's Method for Systems of Equations with Constant Rank Derivatives
AU - Xiubin Xu & Chong Li
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 - <p style="text-align: justify;">The convergence properties of Newton&#39;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&#39;s point estimate theorems as special cases, are obtained.</p>