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Инд. авторы:	Rohn J., Shary S.P.
Заглавие:	Interval matrices: Regularity generates singularity
Библ. ссылка:	Rohn J., Shary S.P. Interval matrices: Regularity generates singularity // Linear Algebra and its Applications. - 2018. - Vol.540. - P.149-159. - ISSN 0024-3795. - EISSN 1873-1856.
Внешние системы:	DOI: 10.1016/j.laa.2017.11.020; РИНЦ: 35496485; SCOPUS: 2-s2.0-85037160769; WoS: 000424178300009;
Реферат:	eng: It is proved that regularity of an interval matrix implies singularity of four related interval matrices. The result is used to prove that for each nonsingular point matrix A, either A or A−1 can be brought to a singular matrix by perturbing only the diagonal entries by an amount of at most 1 each. As a consequence, the notion of a diagonally singularizable matrix is introduced. © 2017
Ключевые слова:	Matrix algebra; Singularity; Absolute value equations; Interval matrix; P-matrices; Regularity; Interval matrix; P-matrix; Regularity; Singularity; Linear algebra; Diagonally singularizable matrix; Absolute value equation; Mathematical techniques;
Издано:	2018
Физ. характеристика:	с.149-159
Цитирование:	1. Kearfott, R., Nakao, M., Neumaier, A., Rump, S., Shary, S., van Hentenryck, P., Standardized notation in interval analysis. Vychisl. Tekhnol. 15:1 (2010), 7-13. 2. Baumann, M., A regularity criterion for interval matrices. Garloff, J., (eds.) Collection of Scientific Papers Honouring Prof. Dr. K. Nickel on Occasion of his 60th Birthday, Part I, 1984, Albert-Ludwigs-Universität, Freiburg, 45-50. 3. Beeck, H., Zur Problematik der Hüllenbestimmung von Intervallgleichungssystemen. Nickel, K., (eds.) Interval Mathematics. Proceedings of the International Symposium, Karlsruhe, West Germany, May 20-24, 1975 Lecture Notes in Comput. Sci., vol. 29, 1975, Springer-Verlag, Berlin, 150-159, 10.1007/3-540-07170-9_12. 4. Rohn, J., Systems of linear interval equations. Linear Algebra Appl. 126 (1989), 39-78, 10.1016/0024-3795(89)90004-9. 5. Rump, S., Verification methods for dense and sparse systems of equations. Herzberger, J., (eds.) Topics in Validated Computations, 1994, North-Holland, Amsterdam, 63-135. 6. Hansen, E., A theorem on regularity of interval matrices. Reliab. Comput. 11:6 (2005), 495-497, 10.1007/s11155-005-0405-9. 7. Rohn, J., Forty necessary and sufficient conditions for regularity of interval matrices: a survey. Electron. J. Linear Algebra 18 (2009), 500-512. 8. Neumaier, A., Interval Methods for Systems of Equations. 1990, Cambridge University Press, Cambridge. 9. Shary, S., Finite-Dimensional Interval Analysis. 2017, XYZ Publishers, Novosibirsk in Russian. 10. Shary, S., On full-rank interval matrices. Numer. Anal. Appl. 7:3 (2014), 241-254, 10.1134/S1995423914030069. 11. Gale, D., Nikaido, H., The Jacobian matrix and global univalence of mappings. Math. Ann. 159 (1965), 81-93, 10.1007/BF01360282. 12. Rohn, J., An algorithm for solving the absolute value equation. Electron. J. Linear Algebra 18 (2009), 589-599.