Geodesic
Convergence of the Newton method with approximation of inverse matrices by the Schulz–Seidel process
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2006), pp. 139-142 
V. M. Verzhbitskiy; N. A. Makurochkina. Convergence of the Newton method with approximation of inverse matrices by the Schulz–Seidel process. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2006), pp. 139-142. http://geodesic.mathdoc.fr/item/IIMI_2006_2_a31/
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     author = {V. M. Verzhbitskiy and N. A. Makurochkina},
     title = {Convergence of the {Newton} method with approximation of inverse matrices by the {Schulz{\textendash}Seidel} process},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For solving systems of non-linear finite-dimensional equations, a modification of the Newton method is proposed which uses consecutive approximation of inverse matrices by the Schulz–Seidel process. Conditions for a quadratic convergence of this method are specified.

[1] Verzhbitskii V. M., Chislennye metody (lineinaya algebra i nelineinye uravneniya), 2-e izd., ONIKS 21 vek, M., 2005, 432 pp.

[2] Verzhbitskii V. M., “Ob iteratsionnom protsesse Shultsa–Zeidelya”, Algoritmicheskii analiz neustoichivykh zadach, Izd-vo Ural. un-ta, Ekaterinburg, 2004, 108–109

[3] Verzhbitskii V. M., “Vybor parametrov v teoremakh skhodimosti odnogo approksimatsionnogo analoga metoda Nyutona”, Zhurn. vychislit. matematiki i mat. fiziki, 15:6 (1975), 1594–1597 | MR