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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| Published in: | Computational mathematics and mathematical physics Vol. 58; no. 6; pp. 840 - 849 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Moscow
Springer Nature B.V
01.06.2018
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| ISSN: | 0965-5425, 1555-6662 |
| Online Access: | Get full text |
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| Abstract | 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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| AbstractList | 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. |
| Author | O V Murav’eva |
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| Copyright | Computational Mathematics and Mathematical Physics is a copyright of Springer, (2018). All Rights Reserved. |
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| DOI | 10.1134/S0965542518060106 |
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| SubjectTerms | Consistency Inequalities Linear equations Linear programming Mathematical analysis Matrix methods |
| Title | Determination of Consistency and Inconsistency Radii for Systems of Linear Equations and Inequalities Using the Matrix l 1 Norm |
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