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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3, Pages 372–384 (Mi zvmmf10165)  

This article is cited in 2 scientific papers (total in 2 papers)

Consistency and inconsistency radii for solving systems of linear equations and inequalities

O. V. Murav'eva

Moscow State Pedagogical University, ul. Malaya Pirogovskaya 1, Moscow, 129991, Russia

Abstract: Problems that reduce to consistency or inconsistency of systems of linear equations or inequalities arise in many divisions of theoretical informatics. The examples are problems in linear programming, machine learning, multicriteria optimization, etc. There exist different stability measures for the property of consistency or inconsistency, and different information constituents are possible (all the input parameters, the coefficient matrix, the vector of constraints). In this paper, variations of all parameters are examined in combination with an additional constraint important in applications, namely, the nonnegativity of feasible points.

Key words: matrix correction, inconsistent systems of linear equations and inequalities, stability of systems of linear equations and inequalities.

DOI: https://doi.org/10.7868/S0044466915030126

Full text: PDF file (233 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:3, 366–377

Bibliographic databases:

UDC: 519.612
MSC: 15A06
Received: 14.01.2014

Citation: O. V. Murav'eva, “Consistency and inconsistency radii for solving systems of linear equations and inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 372–384; Comput. Math. Math. Phys., 55:3 (2015), 366–377

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Volkov, V. I. Erokhin, A. S. Krasnikov, A. V. Razumov, M. N. Khvostov, “Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems”, Comput. Math. Math. Phys., 57:11 (2017), 1757–1770  mathnet  crossref  crossref  isi  elib
    2. O. V. Murav'eva, “Determination of consistency and inconsistency radii for systems of linear equations and inequalities using the matrix $l_1$ norm”, Comput. Math. Math. Phys., 58:6 (2018), 840–849  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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