Geodesic
On the convergence of Newton's method under $\omega ^\star $-conditioned second derivative
Ioannis K. Argyros 1   ; Saïd Hilout 2
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Laboratoire de Mathématiques et Applications Université de Poitiers Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179 86962 Futuroscope Chasseneuil Cedex, France
Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 341-355 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We provide a new semilocal result for the quadratic convergence of Newton's method under $\omega ^\star $-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using $\omega $-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
DOI : 10.4064/am38-3-5
Keywords: provide semilocal result quadratic convergence newtons method under omega star conditioned second chet derivative banach space handle equations where usual lipschitz type conditions verifiable application involving nonlinear integral equations boundary value problems provided turns out similar result using omega conditioned hypotheses provide usable error estimates indicating only linear convergence newtons method

Ioannis K. Argyros  1   ; Saïd Hilout  2

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Laboratoire de Mathématiques et Applications Université de Poitiers Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179 86962 Futuroscope Chasseneuil Cedex, France 
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     title = {On the convergence of {Newton's} method under $\omega ^\star $-conditioned second derivative},
     journal = {Applicationes Mathematicae},
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Ioannis K. Argyros; Saïd Hilout. On the convergence of Newton's method under $\omega ^\star $-conditioned second derivative. Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 341-355. doi: 10.4064/am38-3-5

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