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Article information
2017 , Volume 22, ¹ 2, p.59-66
Rohn J.
A sufficient condition for an interval matrix to have full column rank
We propose a new sufficient condition for an interval matrix to have full column rank which generalizes the former one based on Beeck regularity criterion. Besides, combining the new condition with the former one, we get a “double condition” of full rank that has an increased strength. The results of a computer experiment are presented that show efficiency of the new full rank tests.
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Keywords: interval matrix, full column rank, sufficient condition, double condition
Author(s):
Rohn Jiri
Professor
Position: Professor
Office: Institute of Computer Science Czech Academy of Sciences
Address: 18207, Czech, Prague, Pod vodarenskou vezi, 2
E-mail: rohn@cs.cas.cz
References:
[1] Beeck, H. Zur Problematik der Hullenbestimmung von Intervallgleichungssystemen. Lecture Notes in Computer Science. Interval Mathematics. Berlin: Springer Verlag; 1975: 150–159.
[2] Farhadsefat, R., Lotfi, T., Rohn, J. A note on regularity and positive definiteness of interval matrices. Central European Journal of Mathematics. 2012; (10):322–328.
[3] Horn, R.A., Johnson, C.R. Matrix analysis. 2nd edition. Cambridge: Cambridge University Press; 2013: 661.
[4] Poljak S., Rohn J. Checking robust non-singularity is NP-hard. Mathematics of Control, Signals, and Systems. 1993; (6):1–9.
[5] Rohn, J. A handbook of results on interval linear problems. Technical report No. V-1163. Prague: Institute of Computer Science, Academy of Sciences of the Czech Republic; 2012: 75. Available at: http://uivtx.cs.cas.cz/~rohn/publist/!aahandbook.pdf.
[6] Rohn, J. FULLCOLRANK: a computer program to study whether the interval matrix has full column rank. 2016. Available at: http://uivtx.cs.cas.cz/~rohn/other/fullcolrank.zip.
[7] Shary, S.P. On full-rank interval matrices. NUMERICAL ANALYSIS AND APPLICATIONS. 2014; 7(3):241– 254.
Bibliography link:
Rohn J. A sufficient condition for an interval matrix to have full column rank // Computational technologies. 2017. V. 22. ¹ 2. P. 59-66
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