G. Alefeld and J. Herzberger, Introduction to interval analysis, 1983.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel et al., LA-PACK Users, 1999.

E. Carson and N. J. Higham, Accelerating the solution of linear systems by iterative refinement in three precisions, SIAM J. Sci. Comput, vol.40, issue.2, pp.817-847, 2018.

J. M. Chesneaux and J. Vignes, Les fondements de l'arithmétique stochastique, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, vol.315, pp.1435-1440, 1992.

C. Denis, P. De-oliveira-castro, and E. Petit, Verificarlo: checking floating point accuracy through Monte Carlo Arithmetic, ARITH'23
URL : https://hal.archives-ouvertes.fr/hal-01192668

P. Eberhart, J. Brajard, P. Fortin, and F. Jézéquel, High performance numerical validation using stochastic arithmetic, Reliable Computing, vol.21, pp.35-52, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01254446

P. Eberhart, B. Landreau, J. Brajard, P. Fortin, and F. Jézéquel, Improving CADNA Performance on GPUs, pp.1016-1025, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01858537

P. Eberhart, J. Brajard, P. Fortin, and F. Jézéquel, Estimation of Round-off Errors in OpenMP Codes, IWOMP 2016, vol.9903, pp.3-16, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01380131

M. Frechtling and P. H. Leong, MCALIB: Measuring Sensitivity to Rounding Error with Monte Carlo Programming, ACM TOPLAS, vol.37, issue.2, pp.1-25, 2015.

F. Févotte and B. Lathuilière, Debugging and optimization of HPC programs in mixed precision with the Verrou tool, CRE at SC18, 2018.

S. Graillat, F. Jézéquel, S. Wang, and Y. Zhu, Stochastic arithmetic in multiprecision, Mathematics in Computer Science, vol.5, issue.4, pp.359-375, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01288865

A. Haidar, A. Abdelfattah, M. Zounon, P. Wu, S. Pranesh et al., The design of fast and energy-efficient linear solvers: On the potential of halfprecision arithmetic and iterative refinement techniques, vol.10860, pp.586-600, 2018.

N. Higham, Accuracy and stability of numerical algorithms, 2002.

, IEEE Computer Society: IEEE Standard for Floating-Point Arithmetic, IEEE Standard, pp.754-2008, 2008.

F. Jézéquel and J. M. Chesneaux, CADNA: a library for estimating round-off error propagation, vol.178, pp.933-955, 2008.

U. Kulisch, Advanced Arithmetic for the Digital Computer, 2002.

S. Montan and C. Denis, Numerical verification of industrial numerical codes, ESAIM: Proc, vol.35, pp.107-113, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00765536

J. Vignes, Zéro mathématique et zéro informatique, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, vol.303, pp.997-1000, 1986.

J. Vignes, A stochastic arithmetic for reliable scientific computation, Mathematics and Computers in Simulation, vol.35, issue.3, pp.233-261, 1993.

J. Vignes, Discrete Stochastic Arithmetic for validating results of numerical software, Numerical Algorithms, vol.37, issue.1-4, pp.377-390, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01146498

J. H. Wilkinson, Rounding errors in algebraic processes, vol.32, 1963.