MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions, Journal of Automated Reasoning, vol.7, issue.4, pp.175-205, 2010. ,
DOI : 10.1007/s10817-009-9149-2
Certification of Bounds of Non-linear Functions: The Templates Method, Intelligent Computer Mathematics -MKM, Calculemus, DML, and Systems and Projects, pp.51-65978, 2013. ,
DOI : 10.1007/978-3-642-39320-4_4
URL : https://hal.archives-ouvertes.fr/hal-00932333
Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq, 2011 IEEE 20th Symposium on Computer Arithmetic, pp.243-252, 2011. ,
DOI : 10.1109/ARITH.2011.40
URL : https://hal.archives-ouvertes.fr/inria-00534854
Rigorous Polynomial Approximation Using Taylor Models in Coq, Proceedings of 4th International Symposium on NASA Formal Methods, pp.85-99, 2012. ,
DOI : 10.1007/978-3-642-28891-3_9
URL : https://hal.archives-ouvertes.fr/ensl-00653460
Horner's rule for interval evaluation revisited, Computing, vol.69, issue.1, pp.51-81, 2002. ,
DOI : 10.1007/s00607-002-1448-y
Efficient and accurate computation of upper bounds of approximation errors, Theoretical Computer Science, vol.412, issue.16, pp.1523-1543, 2011. ,
DOI : 10.1016/j.tcs.2010.11.052
URL : https://hal.archives-ouvertes.fr/ensl-00445343
Sollya: An Environment for the Development of Numerical Codes, Proceedings of the 3rd International Congress on Mathematical Software, pp.28-31, 2010. ,
DOI : 10.1007/978-3-642-15582-6_5
URL : https://hal.archives-ouvertes.fr/hal-00761644
Verified Real Number Calculations: A Library for Interval Arithmetic, IEEE Transactions on Computers, vol.58, issue.2, pp.226-237, 2009. ,
DOI : 10.1109/TC.2008.213
URL : https://hal.archives-ouvertes.fr/hal-00168402
Guaranteed Proofs Using Interval Arithmetic, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.188-195 ,
DOI : 10.1109/ARITH.2005.25
URL : https://hal.archives-ouvertes.fr/hal-00164621
Automated Real Proving in PVS via MetiTarski, FM, Lecture Notes in Computer Science, pp.194-199, 2014. ,
DOI : 10.1007/978-3-319-06410-9_14
Global Optimization Using Interval Analysis: Revised And Expanded. Monographs and textbooks in pure and applied mathematics, 2003. ,
Verifying the accuracy of polynomial approximations in HOL, Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, pp.137-152, 1007. ,
DOI : 10.1007/BFb0028391
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
Rigorous Polynomial Approximations and applications, 2011. ,
Rigorous analysis of nonlinear motion in particle accelerators, 1998. ,
Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, vol.4, issue.4, pp.379-456, 2003. ,
Certified, Efficient and Sharp Univariate Taylor Models in COQ, 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, pp.193-200, 2013. ,
DOI : 10.1109/SYNASC.2013.33
URL : https://hal.archives-ouvertes.fr/hal-00845791
Floating-point arithmetic in the Coq system, Proceedings of the 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
Proving Bounds on Real-Valued Functions with Computations, Proceedings of the 4th International Joint Conference on Automated Reasoning, pp.2-17, 2008. ,
DOI : 10.1007/978-3-540-71070-7_2
URL : https://hal.archives-ouvertes.fr/hal-00180138
Floating-point arithmetic in the Coq system, Information and Computation, vol.216, pp.14-23, 2012. ,
DOI : 10.1016/j.ic.2011.09.005
URL : https://hal.archives-ouvertes.fr/hal-00797913
Interval Analysis, 1966. ,
Handbook of Floating-Point Arithmetic, Birkhäuser Boston, pp.978-978, 2010. ,
DOI : 10.1007/978-0-8176-4705-6
URL : https://hal.archives-ouvertes.fr/ensl-00379167
Formalization of Bernstein Polynomials and Applications to Global Optimization, Journal of Automated Reasoning, vol.43, issue.1, pp.151-196, 1007. ,
DOI : 10.1007/s10817-012-9256-3
A Formally Verified Generic Branching Algorithm for Global Optimization, Proceedings of the 5th International Conference on Verified Software: Theories, Tools, Experiments, pp.326-343978, 2013. ,
DOI : 10.1007/978-3-642-54108-7_17
Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations, Proceedings of the 5th International Symposium on NASA Formal Methods, pp.383-397978, 2013. ,
DOI : 10.1007/978-3-642-38088-4_26
Table-driven implementation of the exponential function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software, vol.15, issue.2, pp.144-157, 1989. ,
DOI : 10.1145/63522.214389
Fast evaluation of elementary mathematical functions with correctly rounded last bit, ACM Transactions on Mathematical Software, vol.17, issue.3, pp.410-423, 1991. ,
DOI : 10.1145/114697.116813
Global Optimization in Type Theory, France, 2008. ,