In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.
@article{bwmeta1.element.doi-10_2478_BF02479204, author = {B\'ela Finta}, title = {A Newton-Kantorovich-SOR type theorem}, journal = {Open Mathematics}, volume = {3}, year = {2005}, pages = {282-293}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02479204} }
Béla Finta. A Newton-Kantorovich-SOR type theorem. Open Mathematics, Tome 3 (2005) pp. 282-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479204/
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