Geodesic
Expanding the applicability of two-point Newton-like methods under generalized conditions
Ioannis K. Argyros 1   ; Saïd Hilout 2
1 Cameron University Department of Mathematical Sciences Lawton, OK 73505, U.S.A.
2 Poitiers University Laboratoire de Mathématiques et Applications Bd. Pierre et Marie Curie Téléport 2, B.P. 30179 86962 Futuroscope Chasseneuil Cedex, France
Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 63-90 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied.
DOI : 10.4064/am40-1-4
Keywords: two point newton like method approximate locally unique solution nonlinear equation containing non differentiable term banach space setting using precise majorizing sequences earlier studies present tighter semi local local convergence analysis weaker convergence criteria expand applicability these methods numerical examples provided where old convergence criteria convergence criteria satisfied

Ioannis K. Argyros  1   ; Saïd Hilout  2

1 Cameron University Department of Mathematical Sciences Lawton, OK 73505, U.S.A.
2 Poitiers University Laboratoire de Mathématiques et Applications Bd. Pierre et Marie Curie Téléport 2, B.P. 30179 86962 Futuroscope Chasseneuil Cedex, France 
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Ioannis K. Argyros; Saïd Hilout. Expanding the applicability
 of two-point Newton-like methods
 under generalized conditions. Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 63-90. doi: 10.4064/am40-1-4

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