Geodesic
On the convergence of two-step Newton-type methods of high efficiency index
Ioannis K. Argyros 1   ; Saïd Hilout 2
1 Department of Mathematics 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 36 (2009) no. 4, pp. 465-499 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.
DOI : 10.4064/am36-4-6
Keywords: introduce idea recurrent functions provide semilocal convergence analysis two step newton type methods high efficiency index turns out sufficient convergence conditions weaker error bounds tighter earlier studies many interesting cases applications numerical examples involving nonlinear integral equation chandrasekhar type differential equation containing greens kernel provided

Ioannis K. Argyros  1   ; Saïd Hilout  2

1 Department of Mathematics 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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Ioannis K. Argyros; Saïd Hilout. On the convergence of two-step Newton-type
 methods of high efficiency index. Applicationes Mathematicae, Tome 36 (2009) no. 4, pp. 465-499. doi: 10.4064/am36-4-6

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