[1] R. E. Moore, R. B. Kearfott, and M. J. Cloud, Introduction to interval analysis. Philadelphia, PA: SIAM, 2009.

[2] A. Neumaier, Interval methods for systems of equations. Cambridge: Cambridge University Press, 1990.

[3] V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, Computational complexity and feasibility of data processing and interval
computations. Kluwer, 1998.

[4] J. Rohn, “Checking properties of interval matrices,” Technical Report 686, Institute of Computer Science, Academy of Sciences of
the Czech Republic, Prague, 1996.

[5] J. Rohn, “A handbook of results on interval linear problems,” Technical Report 1163, Institute of Computer Science, Academy of
Sciences of the Czech Republic, Prague, 2012.

[6] D. Hertz, “The extreme eigenvalues and stability of real symmetric interval matrices,” IEEE Trans. Autom. Control, vol. 37, no. 4,
pp. 532–535, 1992.
[Crossref]

[7] M. Hladík, D. Daney, and E. P. Tsigaridas, “Characterizing and approximating eigenvalue sets of symmetric interval matrices,”
Comput. Math. Appl., vol. 62, no. 8, pp. 3152–3163, 2011.
[Web of Science] [Crossref]

[8] Y. Becis-Aubry and N. Ramdani, “State-bounding estimation for nonlinear models with multiple measurements,” in American
Control Conference (ACC 2012), (Montréal, Canada), pp. 1883–1888, IEEE Computer Society, 2012.

[9] M. S. Darup, M. Kastsian, S. Mross, and M. Mönnigmann, “Efficient computation of spectral bounds for hessian matrices on
hyperrectangles for global optimization,” J. Glob. Optim., pp. 1–22, 2013. DOI: 10.1007/s10898-013-0099-1.
[Web of Science] [Crossref]

[10] M. Hladík, D. Daney, and E. Tsigaridas, “Bounds on real eigenvalues and singular values of interval matrices,” SIAM J. Matrix
Anal. Appl., vol. 31, no. 4, pp. 2116–2129, 2010.
[Web of Science] [Crossref]

[11] L. V. Kolev, “Outer interval solution of the eigenvalue problem under general form parametric dependencies,” Reliab. Comput.,
vol. 12, no. 2, pp. 121–140, 2006.

[12] L. V. Kolev, “Determining the positive definiteness margin of interval matrices,” Reliab. Comput., vol. 13, no. 6, pp. 445–466, 2007.
[Web of Science]

[13] M.-H. Matcovschi and O. Pastravanu, “A generalized Hertz-type approach to the eigenvalue bounds of complex interval matrices,”
in IEEE 51st Annual Conference on Decision and Control (CDC 2012), (Hawaii, USA), pp. 2195–2200, IEEE Computer Society,
2012.

[14] O. Beaumont, “An algorithm for symmetric interval eigenvalue problem,” Tech. Rep. IRISA-PI-00-1314, Institut de recherche en
informatique et systèmes aléatoires, Rennes, France, 2000.

[15] M. Hladík, D. Daney, and E. P. Tsigaridas, “A filtering method for the interval eigenvalue problem,” Appl. Math. Comput., vol. 217,
no. 12, pp. 5236–5242, 2011.
[Web of Science]

[16] J. Rohn, “An algorithm for checking stability of symmetric interval matrices,” IEEE Trans. Autom. Control, vol. 41, no. 1,
pp. 133–136, 1996.
[Crossref]

[17] Q. Yuan, Z. He, and H. Leng, “An evolution strategy method for computing eigenvalue bounds of interval matrices,” Appl. Math.
Comput., vol. 196, no. 1, pp. 257–265, 2008.
[Web of Science]

[18] S. Miyajima, T. Ogita, S. Rump, and S. Oishi, “Fast verification for all eigenpairs in symmetric positive definite generalized
eigenvalue problems,” Reliab. Comput., vol. 14, pp. 24–45, 2010.

[19] S. M. Rump, “Verification methods: Rigorous results using floating-point arithmetic,” Acta Numer., vol. 19, pp. 287–449, 2010.
[Web of Science] [Crossref]

[20] J. Rohn, “Checking positive definiteness or stability of symmetric interval matrices is NP-hard,” Commentat. Math. Univ. Carol.,
vol. 35, no. 4, pp. 795–797, 1994.

[21] A. Nemirovskii, “Several NP-hard problems arising in robust stability analysis,” Math. Control Signals Syst., vol. 6, no. 2,
pp. 99–105, 1993.

[22] J. Rohn, “Interval matrices: Singularity and real eigenvalues,” SIAM J. Matrix Anal. Appl., vol. 14, no. 1, pp. 82–91, 1993.

[23] V. Kreinovich, “How to define relative approximation error of an interval estimate: A proposal,” Appl. Math. Sci., vol. 7, no. 5,
pp. 211–216, 2013.

[24] I. C. F. Ipsen, “Relative perturbation results for matrix eigenvalues and singular values,” Acta Numer., vol. 7, pp. 151–201, 1998.
[Crossref]

[25] J. Rohn, “Computing the norm kAk1;1 is NP-hard,” Linear Multilinear Algebra, vol. 47, no. 3, pp. 195–204, 2000.

[26] G. H. Golub and C. F. Van Loan, Matrix computations. Baltimore: Johns Hopkins University Press, 3rd ed., 1996.

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