Exact formula for the solution of degenerate system of quadratic equations

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

Abstract. The paper devoted to the solution of nonlinear system of equations F(x) = 0, where the mapping F is quadratic, acting from nn. 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).

全文:

受限制的访问

作者简介

Yu. Evtushenko

Federal Research Center “Computer Science and Control” of RAS; Moscow Institute of Physics and Technology (National Research University)

编辑信件的主要联系方式.
Email: yuri-evtushenko@yandex.ru
俄罗斯联邦, 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

俄罗斯联邦, Vavilova str., 44, Moscow, 119333; Siedlce, 08-110 Poland

参考

  1. Белаш К.Н., Третьяков А.А. Методы решения вырожденных задач // Ж. вычисл. матем. и матем. физ. 1988. Т. 28. №. 7. С. 1097–1102.
  2. Белаш К.Н. Решение систем нелинейных уравнений общего вида // Ж. вычисл. матем. и матем. физ. 1990. Т. 30. №. 6. С. 837–843.
  3. Измайлов A.Ф., Третьяков А.А. Фактор-анализ нелинейных отображений. М.: Наука, 1994.
  4. 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.
  5. Facchinei F., Fisher A., Kanzow C. On the Accurate Identification of Active Constraints // SIAM J. Optim. 1998. No. 9. P. 14–32.
  6. Измайлов А.Ф., Третьяков А.А. 2-регулярные решения нелинейных задач. Теория и численные методы. М.: Физматлит, 1999.
  7. Брежнева О.А., Третьяков А.А. Новые методы решения существенно нелинейных задач. М.: ВЦ РАН, 2000.

补充文件

附件文件
动作
1. JATS XML

版权所有 © Russian Academy of Sciences, 2024