Geodesic
Local convergence for a family of iterative methods based on decomposition techniques
Ioannis K. Argyros1 ; Santhosh George2 ; Shobha Monnanda Erappa3
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Department of Mathematical and Computational Sciences NIT Karnataka Karnataka, India 575 025
3 Department of Mathematical and Computational Sciences NIT Karnataka India-575 025
Applicationes Mathematicae, Tome 43 (2016) no. 1, pp. 133-143.

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We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz constants. Numerical examples are also provided.
DOI : 10.4064/am2261-12-2015
Keywords: present local convergence analysis family iterative methods obtained using decomposition techniques convergence these methods shown before using hypotheses seventh derivative although only first derivative appears these methods present study expand applicability these methods showing convergence using only first derivative moreover present radius convergence computable error bounds based only lipschitz constants numerical examples provided

Ioannis K. Argyros 1 ; Santhosh George 2 ; Shobha Monnanda Erappa 3

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Department of Mathematical and Computational Sciences NIT Karnataka Karnataka, India 575 025
3 Department of Mathematical and Computational Sciences NIT Karnataka India-575 025 
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Ioannis K. Argyros; Santhosh George; Shobha Monnanda Erappa. Local convergence for a family of iterative methods based on decomposition techniques. Applicationes Mathematicae, Tome 43 (2016) no. 1, pp. 133-143. doi : 10.4064/am2261-12-2015. http://geodesic.mathdoc.fr/articles/10.4064/am2261-12-2015/

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