Author(s):
Herrero Pau
Professor
Position: Professor
Office: Imperial College
Address: United kingdom, London, SW7 2AZ
Phone Office: (440)20 7589 5111
E-mail: p.herrero-vinias@imperial.ac.uk

Sainz Miguel Angel
Office: University of Girona
Address: 17004, Spain, Girona

References:
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[2] Tarski, A. A Decision Method for Elementary Algebra and Geometry. 2nd ed. Berkeley: University of California Press; 1951: 63.
[3] Collins, G. E. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. 2nd GI Conference «Automata Theory and Formal Languages», Kaiserslautern, May 20-23. Lecture Notes in Computer Science. 1975; (33):134-183.
[4] Benhamou, F., Goulard, F. Universally quantified interval constraints. Principles and Practice of Constraint Programming – CP 2000. Proceedings of the 6th International Conference CP 2000, Singapore, September 18–21, 2000. Lecture Notes in Computer Science. 2000; (1894):67–82. DOI: 10.1007/3-540-45349-0_7
[5] Shary, S.P. A new technique in systems analysis under interval uncertainty and ambiguity. Reliable Computing. 2002; 8(5):321–418.
[6] Jaulin, L., Braems, I., Walter, E. Interval methods for nonlinear identification and robust control. Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada USA, December 2002. 2002:4676–4681.
[7] Ratschan, S. Efficient solving of quantified inequality constraints over the real numbers. ACM Transactions on Computational Logic. 2006; 7(4):723–748.
[8] Sharaya, I.A., Shary, S.P. Tolerable solution set for interval linear systems with constraints on coefficients. Reliable Computing. 2011; 15(4):345–357.
[9] Goldsztejn, A., Jaulin, L. Inner approximation of the range of vector-valued functions. Reliable Computing. 2010; (14):1–23.
[10] Herrero, P., Vehı, J., Sainz, M. A., Jaulin, L. Quantified Set Inversion algorithm. Reliable Computing. 2005; 11(5):369–382.
[11] Kreinovich, V., Nesterov, V.M., Zheludeva, N.A. Interval methods that are guaranteed to underestimate (and the resulting new justification of Kaucher arithmetic). Reliable Computing. 1996; 2(2):119–124.
[12] Sainz, M.A., Armengol, J., Calm, R., Herrero, P., Jorba, L., Vehi, J. Modal Interval Analysis. New Tools for Numerical Information. Lecture Notes in Mathematics. 2014; (2091): 316.
[13] Moore, R.E., Kearfott, R.B., Cloud, M.J. Introduction to interval analysis. Philadelphia: SIAM; 2009: 223.
[14] Hansen E., Walster G.W. Global optimization using interval analysis. New York: Marcel Dekker; 2004.
[15] Kaucher, E. Interval analysis in the extended interval space IR. Computing Suppl. 1980; (2):33–49.
[16] Herrero, P., Sainz, M.A. MIC: Model Interval Calculator, 2015. Available at: https://sites.google.com/site/modalintervalcalculator/
[17] Jaulin, L., Walter, E. Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica. 1993; 32(8):1053–1064.
[18] Sharaya, I.A. IntLinInc3D — a software package for visualization of solution sets to interval linear 3D systems. Available at: http://www.nsc.ru/interval/sharaya/
[19] Sharaya, I.A. Boundary Intervals Method for visualization of polyhedral solution sets. Reliable Computing. 2015; 19(4):435–467.
[20] Ratschan, S., Vehı, J. Robust pole clustering of parametric uncertain systems using interval methods. Robust Control Design 2003 (ROCOND 2003): A Proceedings Volume from the 4th IFAC Symposium, Milan, Italy, 25–27 June, 2003. Edited by S. Bittanti and P. Colaneri. International Federation of Automatic Control. 2004: 323–328.
[21] Herrero, P., Georgiou, P., Toumazou, C., Delaunay, B., Jaulin, L. An efficient implementation of SIVIA algorithm in a high-level numerical programming language. Reliable Computing. 2012; (16):239–251.