On the generalization of the Newton–Kantorovich theorem for nonlinear operator equations
UDC 517.98, 519.61 We construct a modification of the classical Newton-Kantorovich method for nonlinear operator equations whose linearization gives equations that are, as a rule, solvable. For finding the solution of a nonlinear operator equation, we propose to use an iterative scheme with quadrati...
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| Дата: | 2026 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9888 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.98, 519.61
We construct a modification of the classical Newton-Kantorovich method for nonlinear operator equations whose linearization gives equations that are, as a rule, solvable. For finding the solution of a nonlinear operator equation, we propose to use an iterative scheme with quadratic convergence. In particular, we establish solvability conditions and construct an iterative procedure aimed at finding the solution of the generalized Riccati equation. |
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| DOI: | 10.3842/umzh.v78i3-4.9888 |