Milan Hladík. AE solutions and AE solvability to general interval linear systems. Linear Algebra Appl., 465(0):221–238, 2015.
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We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so-called AE solutions) and solvability (so-called AE solvability) by using forall-exists quantification of interval parameters. We present an explicit description of the AE solutions, and discuss complexity issues as well. For AE solvability, we propose a sufficient condition only, but for a specific sub-class of problems, a complete characterization is developed. Moreover, we investigate inequality systems for which AE solvability is equivalent to existence of an AE solution.
Page 3, the last line: in (2) should be $b_c$ instead of $B_c$. Page 4, line 3: the general linear system, not only equations, should be displayed. Page 11: superfluous matrix transposition in (14b).
@article{Hla2015a,
author = "Milan Hlad\'{\i}k",
title = "{AE} solutions and {AE} solvability to general interval linear systems",
journal = "Linear Algebra Appl.",
fjournal = "Linear Algebra and its Applications",
volume = "465",
number = "0",
pages = "221-238",
year = "2015",
doi = "10.1016/j.laa.2014.09.030",
issn = "0024-3795",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.laa.2014.09.030",
bib2html_errata = "Page 3, the last line: in (2) should be $b_c$ instead of $B_c$. Page 4, line 3: the general linear system, not only equations, should be displayed. Page 11: superfluous matrix transposition in (14b).",
abstract = "We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so-called AE solutions) and solvability (so-called AE solvability) by using forall-exists quantification of interval parameters. We present an explicit description of the AE solutions, and discuss complexity issues as well. For AE solvability, we propose a sufficient condition only, but for a specific sub-class of problems, a complete characterization is developed. Moreover, we investigate inequality systems for which AE solvability is equivalent to existence of an AE solution.",
keywords = "Interval matrix, Interval analysis, Interval linear system",
}
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