Milan Hladík. Weak and strong solvability of interval linear systems of equations and inequalities. Linear Algebra Appl., 438(11):4156–4165, 2013.
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We consider weak and strong solvability of general interval linear systems consisting of mixed equations and inequalities with mixed free and sign-restricted variables. We generalize the well-known weak solvability characterizations by Oettli-Prager (for equations) and Gerlach (for inequalities) to a unified framework. In the same manner, we extend strong solvability theorems to general interval linear systems. Next, we propose a sufficient condition for checking strong solvability. We give an application in linear programming with interval data. By means of weak and strong solvability we determine limits of the optimal values for any form of the problem setting.
@article{Hla2013b,
author = "Milan Hlad\'{\i}k",
title = "Weak and strong solvability of interval linear systems of equations and inequalities",
journal = "Linear Algebra Appl.",
fjournal = "Linear Algebra and its Applications",
volume = "438",
number = "11",
pages = "4156-4165",
year = "2013",
doi = "10.1016/j.laa.2013.02.012",
issn = "0024-3795",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.laa.2013.02.012",
abstract = "We consider weak and strong solvability of general interval linear systems consisting of mixed equations and inequalities with mixed free and sign-restricted variables. We generalize the well-known weak solvability characterizations by Oettli-Prager (for equations) and Gerlach (for inequalities) to a unified framework. In the same manner, we extend strong solvability theorems to general interval linear systems. Next, we propose a sufficient condition for checking strong solvability. We give an application in linear programming with interval data. By means of weak and strong solvability we determine limits of the optimal values for any form of the problem setting.",
keywords = "Interval matrix, Interval analysis, Interval linear system",
}
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