|
|
|
References
|
|
|
1. |
Bastrakov S. I., Zolotykh N.Yu., “Fast method for verifying Chernikov rules in Fourier–Motzkin elimination”, Computational Mathematics and Mathematical Physics, 55:1 (2015), 160–167 |
2. |
Veselov S. I., Parubochii I. E., Shevchenko V. N., “A program for finding the skeleton of the cone of nonnegative solutions of a system of linear inequalities”, System and applied software, v. 2, Gor'kii State University, Gor'kii, 1984, 83–92 (in Russian) |
3. |
Zolotykh N.Yu., “New modification of the double description method for constructing the skeleton of a polyhedral cone”, Computational Mathematics and Mathematical Physics, 52:1 (2012), 146–156 |
4. |
Mnev N. E., “On realizability of combinatorial types of convex polytopes over number fields”, Zap. Nauchn. Sem. LOMI, 123 (1983), 203–207 (in Russian) |
5. |
Motzkin T. S., Raiffa H., Thompson G. L., Thrall R. M., “The double description method”, Contributions to theory of games, v. 2, Princeton University Press, Princeton, New Jersey, 1953, 51–73 |
6. |
Schrijver A., Theory of linear and integer programming, John Wiley & Sons, 1998 |
7. |
Ziegler G. M., Lectures on polytopes, Springer, New York, 1995, 370 pp. |
8. |
Chernikov S. N., Linear inequalities, Nauka, M., 1968, 488 pp. |
9. |
Chernikova N. V., “Algorithm for finding a general formula for the non-negative solutions of a system of linear inequalities”, USSR Computational Mathematics and Mathematical Physics, 5:2 (1965), 228–233 |
10. |
Avis D., “A revised implementation of the reverse search vertex enumeration algorithm”, Polytopes — combinatorics and computation, Birkhäuser, Basel, 2000, 177–198 |
11. |
Avis D., Bremner D., Seidel R., How good are convex hull algorithms?, Computational Geometry, 7:5–6 (1997), 265–301 |
12. |
Avis D., Fukuda K., “A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra”, Discrete and Computational Geometry, 8:3 (1992), 295–313 |
13. |
Bagnara R., Hill P. M., Zaffanella E., “The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems”, Science of Computer Programming, 72:1–2 (2008), 3–21 |
14. |
Barber C. B., Dobkin D. P., Huhdanpaa H., “The quickhull algorithm for convex hulls”, ACM Transactions on Mathematical Software (TOMS), 22:4 (1996), 469–483 |
15. |
Bremner D., Fukuda K., Marzetta A., “Primal-dual methods for vertex and facet enumeration”, Discrete and Computational Geometry, 20:3 (1998), 333–357 |
16. |
Demenkov M., Filimonov N., “Polyhedral barrier regulator design using non-monotonic Lyapunov function”, 2016 International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), IEEE, 2016 |
17. |
Fukuda K., Prodon A., “Double description method revisited”, Combinatorics and Computer Science, CCS 1995, Lecture Notes in Computer Science, 1120, Springer, Berlin–Heidelberg, 1996, 91–111 |
18. |
Horst R., Pardalos P. M., Van Thoai N., Introduction to global optimization, Springer US, 2000 |
19. |
Loos R., “Computing in algebraic extensions”, Computer Algebra, Computing Supplementa, 4, Springer, Vienna, 1983, 173–187 |
20. |
Perry J., “Exploring the dynamic Buchberger algorithm”, Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC'17, ACM, 2017, 365–372 |
21. |
Rump S., “On the sign of a real algebraic number”, Proceedings of the third ACM symposium on Symbolic and algebraic computation, ACM, 1976, 238–241 |
22. |
Schrijver A., Combinatorial optimization. Polyhedra and efficiency, Springer-Verlag, Berlin–Heidelberg, 2003 |
23. |
Terzer M., Stelling J., “Large-scale computation of elementary flux modes with bit pattern trees”, Bioinformatics, 24:19 (2008), 2229–2235 |