Мақаланы E-mail арқылы жіберу Exact formula for the solution of degenerate system of quadratic equations
- Авторлар: Evtushenko Y.G.1,2, Tret'yakov A.A.1,3
-
Мекемелер:
- Federal Research Center “Computer Science and Control” of RAS
- Moscow Institute of Physics and Technology (National Research University)
- Siedlce University
- Шығарылым: Том 64, № 3 (2024)
- Беттер: 387-391
- Бөлім: General numerical methods
- URL: https://vietnamjournal.ru/0044-4669/article/view/665087
- DOI: https://doi.org/10.31857/S0044466924030012
- EDN: https://elibrary.ru/XHLYYB
- ID: 665087
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Аннотация
Abstract. The paper devoted to the solution of nonlinear system of equations F(x) = 0, where the mapping F is quadratic, acting from . We consider the case, when the derivative F' is degenerate at the solution point. Based on the constructions of the p-regularity theory was proposed a 2-factor method for solving singular system of equations, which converges at a quadratic rate. Moreover, an exact formula is obtained for solving this quadratic system of equations in the 2-regular case of the mapping F(x).
Негізгі сөздер
Толық мәтін
Авторлар туралы
Yu. Evtushenko
Federal Research Center “Computer Science and Control” of RAS; Moscow Institute of Physics and Technology (National Research University)
Хат алмасуға жауапты Автор.
Email: yuri-evtushenko@yandex.ru
Ресей, Vavilova str., 44, Moscow, 119333; Institutskiy per, 1, Dolgoprudnyi, Moscow Region, 141701
A. Tret'yakov
Federal Research Center “Computer Science and Control” of RAS; Siedlce University
Email: prof.tretyakov@gmail.com
Faculty of Exact and Natural Sciences
Ресей, Vavilova str., 44, Moscow, 119333; Siedlce, 08-110 PolandӘдебиет тізімі
- Белаш К.Н., Третьяков А.А. Методы решения вырожденных задач // Ж. вычисл. матем. и матем. физ. 1988. Т. 28. №. 7. С. 1097–1102.
- Белаш К.Н. Решение систем нелинейных уравнений общего вида // Ж. вычисл. матем. и матем. физ. 1990. Т. 30. №. 6. С. 837–843.
- Измайлов A.Ф., Третьяков А.А. Фактор-анализ нелинейных отображений. М.: Наука, 1994.
- Tret’yakov A., Marsden J.E. Factor analysis of nonlinear mappings: p-regularity theory // Communications on Pure & Applied Analysis. 2003. Vol. 2. No. 4. P. 425–445.
- Facchinei F., Fisher A., Kanzow C. On the Accurate Identification of Active Constraints // SIAM J. Optim. 1998. No. 9. P. 14–32.
- Измайлов А.Ф., Третьяков А.А. 2-регулярные решения нелинейных задач. Теория и численные методы. М.: Физматлит, 1999.
- Брежнева О.А., Третьяков А.А. Новые методы решения существенно нелинейных задач. М.: ВЦ РАН, 2000.
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