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Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://num-meth.srcc.msu.ru/english/zhurnal/tom_2016/v17r102.html
Дата изменения: Tue Jan 19 12:41:42 2016 Дата индексирования: Sun Apr 10 02:59:37 2016 Кодировка: IBM-866 |
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"Increasing the interval of convergence for a generalized Newton's method
of solving nonlinear equations" Gromov A.N. |
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An approach to the construction of an extended interval of convergence for a previously proposed generalization of Newton's method to solve nonlinear equations of one variable. This approach is based on the boundedness of a continuous function defined on a segment. It is proved that, for the search for the real roots of a real-valued polynomial with complex roots, the proposed approach provides iterations with nonlocal convergence. This result is generalized to the case transcendental equations. Keywords: iterative processes, Newton's method, logarithmic derivative, continuous functions defined on a segment, higher order methods, interval of convergence, transcendental equations.
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