Milan Hladík. Solution set characterization of linear interval systems with a specific dependence structure. Reliab. Comput., 13(4):361–374, 2007.
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This is a contribution to solvability of linear interval equations and inequalities. In interval analysis we usually suppose that values from different intervals are mutually independent. This assumption can be sometimes too restrictive. In this article we derive extensions of Oettli--Prager theorem and Gerlach theorem for the case where there is a simple dependence structure between coefficients of an interval system. The dependence is given by equality of two submatrices of the constraint matrix.
@article{Hla2007b,
author = "Milan Hlad\'{\i}k",
title = "Solution set characterization of linear interval systems with a~specific dependence structure",
webtitle = "Solution set characterization of linear interval systems with a specific dependence structure",
journal = "Reliab. Comput.",
fjournal = "Reliable Computing",
volume = "13",
number = "4",
pages = "361-374",
year = "2007",
doi = "10.1007/s11155-007-9033-x",
url = "https://doi.org/10.1007/s11155-007-9033-x",
bib2html_dl_html = "https://link.springer.com/article/10.1007/s11155-007-9033-x",
bib2html_dl_pdf = "https://kam.mff.cuni.cz/~hladik/doc/2007solSetSep-RC.pdf",
abstract = "This is a contribution to solvability of linear interval equations and inequalities. In interval analysis we usually suppose that values from different intervals are mutually independent. This assumption can be sometimes too restrictive. In this article we derive extensions of Oettli--Prager theorem and Gerlach theorem for the case where there is a simple dependence structure between coefficients of an interval system. The dependence is given by equality of two submatrices of the constraint matrix.",
keywords = "interval systems, interval matrix, weak solution",
}
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