Milan Hladík. Transformations of interval linear systems of equations and inequalities. Linear Multilinear Algebra, 65(2):211–223, 2017.
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Very recently, new results on transformation of interval linear systems and on generalizations of the Farkas lemma to interval systems appeared in the literature. They are by far not obvious since the standard transformations on linear systems are not easily adapted to interval system due to the dependency problem. The aim of this paper was to come up with new possible transformations and to extend the results to more general classes of AE interval systems and to linear parametric systems. We also show that the transformations can help in simplifying the proofs of some characterization theorems.
In Thms. 3.1, 3.2, 3.3, 5.1, 5.2, 6.1 and 6.2, the equivalences hold not only for weak solvability, but also for the weak solution sets themselves. In the left-hand sides of (5) and (6), there should be the minus sign by b, and accordingly in the proof of Theorem 3.3.
@article{Hla2017a,
author = "Milan Hlad\'{\i}k",
title = "Transformations of interval linear systems of equations and inequalities",
journal = "Linear Multilinear Algebra",
fjournal = "Linear and Multilinear Algebra",
volume = "65",
number = "2",
pages = "211-223",
year = "2017",
doi = "10.1080/03081087.2016.1180339",
issn = "0308-1087",
bib2html_dl_html = "http://dx.doi.org/10.1080/03081087.2016.1180339",
abstract = "Very recently, new results on transformation of interval linear systems and on generalizations of the Farkas lemma to interval systems appeared in the literature. They are by far not obvious since the standard transformations on linear systems are not easily adapted to interval system due to the dependency problem. The aim of this paper was to come up with new possible transformations and to extend the results to more general classes of AE interval systems and to linear parametric systems. We also show that the transformations can help in simplifying the proofs of some characterization theorems.",
bib2html_errata = "In Thms. 3.1, 3.2, 3.3, 5.1, 5.2, 6.1 and 6.2, the equivalences hold not only for weak solvability, but also for the weak solution sets themselves. In the left-hand sides of (5) and (6), there should be the minus sign by b, and accordingly in the proof of Theorem 3.3.",
keywords = "Linear equations; Linear inequalities; Interval analysis; Farkas lemma",
}
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