C. Bendsten and O. Stauning, TADIFF, a Flexible C++ Package for Automatic Differentiation Using Taylor Series, 1997.

Y. Bertot and P. Castéran, Interactive Theorem Proving and Program Development: Coq'Art: the Calculus of Inductive Constructions, 2004.
DOI : 10.1007/978-3-662-07964-5

URL : https://hal.archives-ouvertes.fr/hal-00344237

R. P. Brent, Algorithms for minimization without derivatives, N.J, 1973.

E. W. Cheney, Introduction to Approximation Theory, 1966.

S. Chevillard, . Ch, and . Lauter, A Certified Infinite Norm for the Implementation of Elementary Functions, Seventh International Conference on Quality Software (QSIC 2007), pp.153-160, 2007.
DOI : 10.1109/QSIC.2007.4385491

URL : https://hal.archives-ouvertes.fr/ensl-00119810

M. Daumas, G. Melquiond, and C. Muñoz, Guaranteed Proofs Using Interval Arithmetic, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.188-195, 2005.
DOI : 10.1109/ARITH.2005.25

URL : https://hal.archives-ouvertes.fr/hal-00164621

L. Fousse, Intégration numérique avec erreur bornée en précision arbitraire, 2006.

A. Griewank, Evaluating Derivatives -Principles and Techniques of Algorithmic Differentiation, 2000.

M. Grimmer, K. Petras, and N. , Multiple Precision Interval Packages: Comparing Different Approaches, In Lecture Notes in Computer Science, vol.2991, pp.64-90, 2004.
DOI : 10.1007/978-3-540-24738-8_4

URL : https://hal.archives-ouvertes.fr/inria-00071744

DOI : 10.1016/B978-0-12-505630-4.50021-3

J. Harrison, HOL Light: A tutorial introduction, Proceedings of the First International Conference on Formal Methods in Computer-Aided Design (FMCAD'96), pp.265-269, 1996.
DOI : 10.1007/BFb0031814

J. Harrison, Verifying Nonlinear Real Formulas Via Sums of Squares, Proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, pp.102-118, 2007.
DOI : 10.1007/978-3-540-74591-4_9

W. Hofschuster and W. Krämer, FI_LIB, eine schnelle und portable Funktionsbibliothek für reelle Argumente und reelle Intervalle im IEEE-double-Format, 1998.

B. Kearfott, Rigorous Global Search: Continuous Problems, 1996.
DOI : 10.1007/978-1-4757-2495-0

R. Baker and . Kearfott, Globsol: History, composition, and advice on use, Global Optimization and Constraint Satisfaction, pp.17-31, 2003.

W. Krämer, Sichere und genaue Abschätzung des Approximationsfehlers bei rationalen Approximationen, 1996.

V. Lefèvre and J. Muller, Worst cases for correct rounding of the elementary functions in double precision, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, pp.111-118, 2001.
DOI : 10.1109/ARITH.2001.930110

G. Melquiond, Floating-point arithmetic in the Coq system, RNC 8 Proceedings, 8th Conference on Real Numbers and Computers, pp.93-102, 2008.
DOI : 10.1016/j.ic.2011.09.005

URL : https://hal.archives-ouvertes.fr/hal-00797913

F. Messine, Méthodes d'optimisation globale basées sur l'analyse d'intervalle pour la résolution des problèmes avec contraintes, 1997.

R. E. Moore, Methods and Applications of Interval Analysis, Society for Industrial Mathematics, 1979.
DOI : 10.1137/1.9781611970906

M. Neher, ACETAF: A software package for computing validated bounds for Taylor coefficients of analytic functions, ACM Transactions on Mathematical Software, 2003.

A. Neumaier, Interval Methods for Systems of Equations, 1990.
DOI : 10.1017/CBO9780511526473

A. Neumaier, Taylor forms?use and limits, Reliable Computing, vol.9, issue.1, pp.43-79, 2003.
DOI : 10.1023/A:1023061927787

S. Owre, J. M. Rushby, and N. Shankar, PVS: A prototype verification system, 11th International Conference on Automated Deduction (CADE), pp.748-752, 1992.
DOI : 10.1007/3-540-55602-8_217

F. Rouillier and P. Zimmermann, Efficient isolation of a polynomial real roots, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072518

F. Rouillier and P. Zimmermann, Efficient isolation of polynomial's real roots, Journal of Computational and Applied Mathematics, vol.162, issue.1, pp.33-50, 2004.
DOI : 10.1016/j.cam.2003.08.015

R. Zumkeller, Formal Global Optimization with Taylor Models, IJCAR 2008 -Proceedings of the 4th International Joint Conference on Automated Reasoning, pp.408-422, 2008.
DOI : 10.1007/11814771_35

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=