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Article information
2005 , Volume 10, ¹ 3, p.72-86
Mikheev S.E.
Convergence of Newton's method in different classes of functions
Convergences of the iterative Newton's method for systems of nonlinear equations g(x)=0 with functions g having Lipschitz' constant L versus functions g having local Lipschitz' constant L(x) are compared. For the second class of functions the results similar to the Kantorovich (TK) theorems for C{1,1}(D) are obtained. It is shown that the second class has elements and initial approximations which do not guarantee convergence while the TK do. Vice versa, the class C{1,1} has elements and initial approximations that guarantee the convergence according to the TK, but they do not satisfy the conditions of the theorems presented here.
[full text] Author(s):
Mikheev Serguei Eugenievich
Dr. , Professor
Position: Associate Professor
Office: St. Petersburg State University
Address: 198504, Russia, St-Petersburg, SPb, Universitetskiy pr., 35
Phone Office: (812) 428 42 91
E-mail: him2@mail.ru
Bibliography link:
Mikheev S.E. Convergence of Newton's method in different classes of functions // Computational technologies. 2005. V. 10. ¹ 3. P. 72-86
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