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Volume 4, Issue 1
On Newton's Method for Solving Nonlinear Equations and Function Splitting

Ioannis K. Argyros & Saïd Hilout

DOI: 10.4208/nmtma.2011.m99009

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 53-67.

Published online: 2011-04

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  • Abstract

We provided in [14] and [15] a semilocal convergence analysis for Newton's method on a Banach space setting, by splitting the given operator. In this study, we improve the error bounds, order of convergence, and simplify the sufficient convergence conditions. Our results compare favorably with the Newton-Kantorovich theorem for solving equations.

  • Keywords

Newton's method, Banach space, majorizing sequence, semilocal convergence, splitting of an operator.

  • AMS Subject Headings

65H99, 65H10, 65G99, 49M15, 47J20, 47H04, 90C30, 90C33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-53, author = {}, title = {On Newton's Method for Solving Nonlinear Equations and Function Splitting}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {1}, pages = {53--67}, abstract = {

We provided in [14] and [15] a semilocal convergence analysis for Newton's method on a Banach space setting, by splitting the given operator. In this study, we improve the error bounds, order of convergence, and simplify the sufficient convergence conditions. Our results compare favorably with the Newton-Kantorovich theorem for solving equations.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m99009}, url = {http://global-sci.org/intro/article_detail/nmtma/5958.html} }
TY - JOUR T1 - On Newton's Method for Solving Nonlinear Equations and Function Splitting JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 53 EP - 67 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m99009 UR - https://global-sci.org/intro/article_detail/nmtma/5958.html KW - Newton's method, Banach space, majorizing sequence, semilocal convergence, splitting of an operator. AB -

We provided in [14] and [15] a semilocal convergence analysis for Newton's method on a Banach space setting, by splitting the given operator. In this study, we improve the error bounds, order of convergence, and simplify the sufficient convergence conditions. Our results compare favorably with the Newton-Kantorovich theorem for solving equations.

Ioannis K. Argyros & Saïd Hilout. (2020). On Newton's Method for Solving Nonlinear Equations and Function Splitting. Numerical Mathematics: Theory, Methods and Applications. 4 (1). 53-67. doi:10.4208/nmtma.2011.m99009
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