Geodesic
Inexact Newton methods and recurrent functions
Ioannis K. Argyros 1   ; Saïd Hilout 2
1 Department of Mathematics Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Laboratoire de Mathématiques et Applications Poitiers University Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179 86962 Futuroscope Chasseneuil Cedex, France
Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 113-126 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner//outer iterations can be obtained. Furthermore, numerical examples are provided using polynomial, integral and differential equations.
DOI : 10.4064/am37-1-8
Keywords: provide semilocal convergence analysis approximating solution equation banach space setting using inexact newton method using recurrent functions provide under weaker hypotheses finer error bounds distances involved least precise information location solution earlier papers moreover splitting method smaller number inner outer iterations obtained furthermore numerical examples provided using polynomial integral differential equations

Ioannis K. Argyros  1   ; Saïd Hilout  2

1 Department of Mathematics Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Laboratoire de Mathématiques et Applications Poitiers University Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179 86962 Futuroscope Chasseneuil Cedex, France 
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 recurrent functions
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Ioannis K. Argyros; Saïd Hilout. Inexact Newton methods and
 recurrent functions. Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 113-126. doi: 10.4064/am37-1-8

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