摘要
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.
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.
基金
Acknowledgments. This work was supported in part by the National Natural Science Foundation of China （Grant No. 10671175） and Program for New Century Excellent Talents in Universities. The first author was also supported in part by the Education Ministry of Zhejiang Province （Grant No. 20060492）.
