Determination of Consistency and Inconsistency Radii for Systems of Linear Equations and Inequalities Using the Matrix l 1 Norm

The problem of determining the minimal change in the coefficients of a consistent system of linear equations and inequalities that makes the system inconsistent is considered (the problem of determining the consistency radius of a system). If the original system is inconsistent, the inconsistency ra...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 58; no. 6; pp. 840 - 849
Main Author: O V Murav’eva
Format: Journal Article
Language:English
Published: Moscow Springer Nature B.V 01.06.2018
Subjects:
Consistency
Inequalities
Linear equations
Linear programming
Mathematical analysis
Matrix methods
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:The problem of determining the minimal change in the coefficients of a consistent system of linear equations and inequalities that makes the system inconsistent is considered (the problem of determining the consistency radius of a system). If the original system is inconsistent, the inconsistency radius is defined as the solution to the problem of minimal correction of the coefficients upon which the system has a solution. For a homogeneous system of linear equations and inequalities, it is considered whether the property that a nonzero solution exists changes when correcting the parameters. A criterion for the correction magnitude is the sum of the moduli of all elements of the correction matrix. The problems of determining the consistency and inconsistency radii for systems of linear constraints written in different forms (with equality or inequality constraints and with the condition that some of the variables or all of them are nonnegative) reduce to a collection of finitely many linear programming problems.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542518060106