Convergence of Directional Methods under mild differentiability and applications |
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| Authors: | Ioannis K Argyros Saïd Hilout |
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| Institution: | a Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USA
b 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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| Abstract: | A semilocal convergence analysis for Directional Methods under mild differentiability conditions is provided in this study. Using our idea of recurrent functions, we provide sufficient convergence conditions as well as the corresponding errors bounds. The results are extended to hold in a Hilbert space setting and a favorable comparison is provided with earlier works 6], 7], 8], 9], 10], 11] and 20]. Numerical examples are also provided in this study. |
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| Keywords: | Directional Method Systems of equations Mild differentiability Hilbert space Banach space |
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