Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory

Authors:
Chong Li;Nuchun Hu;Jinhua Wang
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China and Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia;Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, Zhejiang University of Technology, Hangzhou 310032, PR China
Venue:
Journal of Complexity
Year:
2010

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Abstract

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton's method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton's method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also obtained. Applications to some special cases such as the Kantorovich type conditions, @c-conditions and the Smale point estimate theory are provided and some important known results are extended and/or improved.