Geodesic
Linear interval equations with symmetric solution sets
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 562-569 
L. T. Ashchepkov. Linear interval equations with symmetric solution sets. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 562-569. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Criteria for symmetry and boundedness are found for the combined solution set of a system of linear algebraic equations with interval coefficients. It is shown that the problem of the best inner interval estimation of a symmetric solution set can be exactly solved by linear programming methods.

[1] Sharyi S. P., Intervalnye algebraicheskie zadachi i ikh chislennoe reshenie, Dis. $\dots$ d-ra fiz.-matem. nauk, VTs SO RAN, Novosibirsk, 2000, 322 pp.

[2] Jaussern C., “Calculation of exact bounds for the solution set of linear interval systems”, Linear Algebra and its Applic., 251 (1997), 321–340 | DOI | MR

[3] Poljak S., Rohn J., “Cheking robust nonsingularity is NP-hard”, Math. of Control Signals and Systems, 6 (1993), 1–9 | DOI | MR | Zbl

[4] Rohn J., Kreinovich V., “Computing exact componentwise bounds on solutions of linear systems with interval data is NP-hard”, SIAM J. Matr. Analys. Appl., 6 (1995), 415–420 | DOI | MR

[5] Oettli W., Prager W., “Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides”, Numer. Math., 6 (1964), 405–409 | DOI | MR | Zbl

[6] Aschepkov L. T., “O postroenii maksimalnogo kuba, vpisannogo v zadannuyu oblast”, Zh. vychisl. matem. i matem. fiz., 30:2 (1980), 510–513

[7] Aschepkov L. T., Badam U., Modeli i metody povysheniya zhivuchesti upravlyaemykh sistem, Dalnauka, Vladivostok, 2006