MAJORIZING SEQUENCES FOR NEWTON'S METHOD
Keywords:Nonlinear equations in Banach spaces,, Newt9n's method, majorizing sequences
Majorizing sequences for Newton's method are analysed from a new standpoint. As a consequence, we give convergence results under assumptions different from the classical Kantorovich conditions.
L. V. Kantorovich and G. P. Akilov, "Functional Analysis," Pergamon Press, Oxford, 1982.
W. C. Rheinholdt, "A unified convergence theory for a class of iterative process," SIAM J. Numer. Anal., 5(1968), 42-63.
L. B. Rall, "Computational solution of nonlinear operator equations," Robert E. Krieger Publishing Company, Inc., New York, 1979.
J. M. Gutierrez, M. A. Hernandez and M. A. Salanova, "Accesibility of solutions by Newton's method," Inter. J. Computer Math., 57(1995), 239-247.
A. M. Ostrowski, "Solution of equations and systems of equations," Academic Press, New York, 1973.
J. F. Traub, "Iterative methods for solution of equations," Prentice-Hall, New Jersey, 1964.
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