Proyecciones
Vol. 25, No 3, pp. 293-306, December 2006.
Universidad Católica del Norte
Antofagasta - Chile

CONVERGENCE OF NEWTON’S METHOD UNDER THE GAMMA CONDITION

IOANNIS K. ARGYROS

CAMERON UNIVERSITY, U.S.A.

Abstract

We provide a semilocal as well as a local convergence analysis ofNewton’s method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]—[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances involved and an at least as precise informationon the location of the solution; in the local case: a largerradius of convergence.

AMS (MOS) Subject Classification Codes : 65H10, 65G99,47H17, 49M15.

Key Words: Banach space, Newton’s method, local/semilocalconvergence, Newton—Kantorovich theorem, Fréchet derivative, majorizingsequence, radius of convergence, gamma condition, analyticoperator.

REFERENCES

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Ioannis K. Argyros
Department of Mathematical Sciences
Cameron University
Lawton, OK 73505
U. S. A.
e-mail address : iargyros@cameron.edu

Received : April 2006. Accepted : October 2006