Jaroslav Horáček, Jan Horáček, and Milan Hladík. Detecting unsolvability of interval linear systems. In N. Damouche M. Martel and J. A. Dit Sandretto, editors, TNC'18. Trusted Numerical Computations, Kalpa Publications in Computing, pp. 54–69, EasyChair, 2018.
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In this paper we deal with detection of unsolvability of interval linear systems. Various methods based on existing algorithms or on existing sufficient conditions are developed. The methods are tested on a large variety of random systems and the results are visualized. The two strongest sufficient conditions are proved to be equivalent under a certain assumption. The topic of detecting solvability is also touched upon.
@inCollection{HorHor2018a,
author = "Jaroslav Hor\'{a}{\v{c}}ek and Jan Hor\'{a}{\v{c}}ek and Milan Hlad\'{\i}k",
title = "Detecting unsolvability of interval linear systems",
editor = "M. Martel, N. Damouche and J. A. Dit Sandretto",
feditor = "Matthieu Martel and Nasrine Damouche and Julien Alexandre Dit Sandretto",
booktitle = "TNC'18. Trusted Numerical Computations",
publisher = "EasyChair",
series = "Kalpa Publications in Computing",
volume = "8",
pages = "54-69",
year = "2018",
doi = "10.29007/ptx4",
issn = "2515-1762",
url = "https://easychair.org/publications/paper/ZNM2",
bib2html_dl_html = "https://doi.org/10.29007/ptx4",
abstract = "In this paper we deal with detection of unsolvability of interval linear systems. Various methods based on existing algorithms or on existing sufficient conditions are developed. The methods are tested on a large variety of random systems and the results are visualized. The two strongest sufficient conditions are proved to be equivalent under a certain assumption. The topic of detecting solvability is also touched upon.",
keywords = "Full column rank; Interval linear systems; Unsolvability; Unsolvability gap",
}
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