Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 12, Pages 2086–2101
DOI: https://doi.org/10.1134/S0044466919120093 (Mi zvmmf10999) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Newton-type method for solving systems of linear equations and inequalities

A. I. Golikovab, Yu. G. Evtushenkoab, I. E. Kaporinab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
b Moscow Institute of Physics and Technology (State University)
Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.1134/S0044466919120093
Abstract: A Newton-type method is proposed for numerical minimization of convex piecewise quadratic functions, and its convergence is analyzed. Previously, a similar method was successfully applied to optimization problems arising in mesh generation. It is shown that the method is applicable to computing the projection of a given point onto the set of nonnegative solutions of a system of linear equations and to determining the distance between two convex polyhedra. The performance of the method is tested on a set of problems from the NETLIB repository.
Key words: systems of linear equations and inequalities, regularization, penalty function method, duality, projection of a point, piecewise quadratic function, Newton’s method, preconditioned conjugate gradient method.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00510
This work was supported in part by the Russian Foundation for Basic Research, project no. 17-07-00510.
Received: 27.06.2019
Revised: 27.06.2019
Accepted: 05.08.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 12, Pages 2017–2032
DOI: https://doi.org/10.1134/S0965542519120091
Bibliographic databases:
Document Type: Article
UDC: 7.977
Language: Russian
Citation: A. I. Golikov, Yu. G. Evtushenko, I. E. Kaporin, “Newton-type method for solving systems of linear equations and inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 59:12 (2019), 2086–2101; Comput. Math. Math. Phys., 59:12 (2019), 2017–2032
Citation in format AMSBIB
\Bibitem{GolEvtKap19}
\by A.~I.~Golikov, Yu.~G.~Evtushenko, I.~E.~Kaporin
\paper Newton-type method for solving systems of linear equations and inequalities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
\vol 59
\issue 12
\pages 2086--2101
\mathnet{http://mi.mathnet.ru/zvmmf10999}
\crossref{https://doi.org/10.1134/S0044466919120093}
\elib{https://elibrary.ru/item.asp?id=41240360}
\transl
\jour Comput. Math. Math. Phys.
\yr 2019
\vol 59
\issue 12
\pages 2017--2032
\crossref{https://doi.org/10.1134/S0965542519120091}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000514816500008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85079705070}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf10999
  • https://www.mathnet.ru/eng/zvmmf/v59/i12/p2086
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024