Radii of solvability and unsolvability of linear systems

Radii of solvability and unsolvability of linear systems We consider a problem of determining the component-wise distance (called the radius) of a linear system of equations or inequalities to a system that is either solvable or unsolvable. We propose explicit characterization of these radii and show relations between them. Then the radii are classified in the polynomial vs. NP-hard manner. We also present a generalization to an arbitrary linear system consisting from both equations and inequalities with both free and nonnegative variables. Eventually, we extend the concept of the component-wise distance to a non-uniform one. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Linear Algebra and its Applications Elsevier

Radii of solvability and unsolvability of linear systems

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Publisher
Elsevier
Copyright
Copyright © 2016 Elsevier Inc.
ISSN
0024-3795
eISSN
1873-1856
D.O.I.
10.1016/j.laa.2016.03.028
Publisher site
See Article on Publisher Site

Abstract

We consider a problem of determining the component-wise distance (called the radius) of a linear system of equations or inequalities to a system that is either solvable or unsolvable. We propose explicit characterization of these radii and show relations between them. Then the radii are classified in the polynomial vs. NP-hard manner. We also present a generalization to an arbitrary linear system consisting from both equations and inequalities with both free and nonnegative variables. Eventually, we extend the concept of the component-wise distance to a non-uniform one.

Journal

Linear Algebra and its ApplicationsElsevier

Published: Aug 15, 2016

References

  • A note on dependency between interval linear systems
    Li, W.

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