2010
DOI: 10.1007/s11075-010-9368-y
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Abstract: A semilocal convergence analysis for directional two-step Newton methods in a Hilbert space setting is provided in this study. Two different techniques are used to generate the sufficient convergence results, as well as the corresponding error bounds. The first technique uses our new idea of recurrent functions, whereas the second uses recurrent sequences. We also compare the results of the two techniques.

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Cited by 20 publications
(22 citation statements)
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References 11 publications
(31 reference statements)
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“…which shows equation (23) Using equation (15) we get that ( ) 3 The radius r A was shown by us to be the convergence radius of Newton's method (Amat et al, 2008;Argyros, 2008;Argyros and Hilout, 2010) ( ) ( ) under the conditions (15) and (16). It follows from the definition of r that the convergence radius r of the method (2) cannot be larger than the convergence radius r A of the second order Newton's method.…”
Section: Local Convergence Analysismentioning
confidence: 90%
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“…which shows equation (23) Using equation (15) we get that ( ) 3 The radius r A was shown by us to be the convergence radius of Newton's method (Amat et al, 2008;Argyros, 2008;Argyros and Hilout, 2010) ( ) ( ) under the conditions (15) and (16). It follows from the definition of r that the convergence radius r of the method (2) cannot be larger than the convergence radius r A of the second order Newton's method.…”
Section: Local Convergence Analysismentioning
confidence: 90%
“…It follows from equation (24) and the Banach Lemma on invertible functions (Argyros, 2008;Argyros and Hilout, 2010;Ye et al, 2007;Wang and Kou, 2012a) that, F′(x 0 ) ≠ 0 and ( ) ( )…”
Section: Local Convergence Analysismentioning
confidence: 99%
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