Inexact Newton-type methods
We introduce the new idea of recurrent functions to provide a semilocal convergence analysis for an inexact Newton-type method, using outer inverses. It turns out that our sufficient convergence conditions are weaker than in earlier studies in many interesting cases (Argyros, 2004 [5,6], Argyros, 2007 [7], Dennis, 1971 [14], Deuflhard and Heindl, 1979 [15], Gutierrez, 1997 [16], Gutierrez et al., 1995 [17], Haubler, 1986 [18], Huang, 1993 [19], Kantorovich and Akilov, 1982 [20], Nashed and Chen, 1993 [21], Potra, 1982 [22], Potra, 1985[23]). (C) 2010 Elsevier Inc. All rights reserved.
inexact newton-type method recurrent functions semilocal convergence newton's method banach space