Geodesic
A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses
Ioannis K. Argyros1
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
Applicationes Mathematicae, Tome 32 (2005) no. 1, pp. 37-49.

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The Newton–Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton–Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton–Kantorovich hypothesis is violated.
DOI : 10.4064/am32-1-3
Keywords: newton kantorovich approach majorant principle provide local semilocal convergence results newton like methods using outer generalized inverses banach space setting using conditions before provide precise information location solution error bounds distances involved moreover since newton kantorovich type hypothesis weaker before cover cases where original newton kantorovich hypothesis violated

Ioannis K. Argyros 1

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A. 
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Ioannis K. Argyros. A convergence analysis of Newton-like
 methods for singular equations using
 outer or generalized inverses. Applicationes Mathematicae, Tome 32 (2005) no. 1, pp. 37-49. doi : 10.4064/am32-1-3. http://geodesic.mathdoc.fr/articles/10.4064/am32-1-3/

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