A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses
Volume 32 / 2005
Applicationes Mathematicae 32 (2005), 37-49 MSC: 65H10, 65J15, 65G99, 65B05, 65N30, 47H17, 49M15. DOI: 10.4064/am32-1-3
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.