M. Baudin, Error bounds of complex arithmetic, 2011.

R. P. Brent, C. Percival, and P. Zimmermann, Error bounds on complex floating-point multiplication, Mathematics of Computation, vol.76, issue.259, pp.1469-1481, 2007.
DOI : 10.1090/S0025-5718-07-01931-X

URL : https://hal.archives-ouvertes.fr/inria-00120352

R. P. Brent and P. Zimmerman, Modern Computer Arithmetic, 2010.
DOI : 10.1017/CBO9780511921698

URL : https://hal.archives-ouvertes.fr/cel-01500109

N. Brunie, Contributions to Computer Arithmetic and Applications to Embedded Systems, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01078204

W. P. Champagne, On finding roots of polynomials by hook or by crook, 1964.

R. M. Corless and N. Fillion, A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis, 2013.

M. Cornea, J. Harrison, and P. T. Tang, Scientific Computing on Itanium R -based Systems, 2002.

T. J. Dekker, A floating-point technique for extending the available precision, Numerische Mathematik, vol.5, issue.3, pp.224-242, 1971.
DOI : 10.1007/BF01397083

J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
DOI : 10.1137/1.9781611971446

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, vol.23, issue.1, pp.5-48, 1991.
DOI : 10.1145/103162.103163

S. Graillat, V. Lefèvre, and J. M. Muller, On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic, Numerical Algorithms, vol.52, issue.1, pp.11075-11090, 2015.
DOI : 10.1007/s11075-015-9967-8

URL : https://hal.archives-ouvertes.fr/ensl-00945033

J. R. Hauser, Handling floating-point exceptions in numeric programs, ACM Transactions on Programming Languages and Systems, vol.18, issue.2, pp.139-174, 1996.
DOI : 10.1145/227699.227701

N. J. Higham, Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia , second edn, 2002.

N. J. Higham, N. J. Higham, M. R. Dennis, P. Glendinning, P. A. Martin et al., 2. Floating Point Arithmetic, The Princeton Companion to Applied Mathematics, pp.96-97, 2015.
DOI : 10.1137/1.9780898718027.ch2

J. E. Holm, Floating-Point Arithmetic and Program Correctness Proofs, 1980.

C. P. Jeannerod, A radix-independent error analysis of the Cornea-Harrison-Tang method, to appear in ACM Software; preprint available at https, Trans. Math

C. P. Jeannerod, P. Kornerup, N. Louvet, and J. M. Muller, Error bounds on complex floating-point multiplication with an FMA, to appear in Mathematics of Computation , preprint available at https

C. P. Jeannerod, N. Louvet, and J. M. Muller, Further analysis of Kahan???s algorithm for the accurate computation of $2\times 2$ determinants, Mathematics of Computation, vol.82, issue.284, pp.2245-2264, 2013.
DOI : 10.1090/S0025-5718-2013-02679-8

C. P. Jeannerod, N. Louvet, J. M. Muller, and A. Plet, A library for symbolic floating-point arithmetic (2015), preprint available at https

C. P. Jeannerod, N. Louvet, J. M. Muller, and A. Plet, Sharp error bounds for complex floating-point inversion (2015), preprint available at https

C. P. Jeannerod and S. M. Rump, Improved Error Bounds for Inner Products in Floating-Point Arithmetic, SIAM Journal on Matrix Analysis and Applications, vol.34, issue.2, pp.338-344, 2013.
DOI : 10.1137/120894488

URL : https://hal.archives-ouvertes.fr/hal-00840926

C. P. Jeannerod and S. M. Rump, On relative errors of floating-point operations: optimal bounds and applications (2014), preprint available at https

W. Kahan, Pracniques: further remarks on reducing truncation errors, Communications of the ACM, vol.8, issue.1, p.40, 1965.
DOI : 10.1145/363707.363723

D. E. Knuth, The Art of Computer Programming Seminumerical Algorithms, 1998.

O. Møller, Quasi double-precision in floating point addition, BIT, vol.7, issue.6, pp.37-50, 1965.
DOI : 10.1007/BF01975722

D. Monniaux, The pitfalls of verifying floating-point computations, ACM Transactions on Programming Languages and Systems, vol.30, issue.3, pp.1-1241, 2008.
DOI : 10.1145/1353445.1353446

URL : https://hal.archives-ouvertes.fr/hal-00128124

J. M. Muller, using Cornea, Harrison and Tang's Method, ACM Transactions on Mathematical Software, vol.41, issue.2, pp.1-78, 2015.
DOI : 10.1145/2629615

J. M. Muller, N. Brisebarre, F. De-dinechin, C. P. Jeannerod, V. Lefèvre et al., Handbook of Floating-Point Arithmetic, 2010.
DOI : 10.1007/978-0-8176-4705-6

URL : https://hal.archives-ouvertes.fr/ensl-00379167

T. Ogita, S. M. Rump, and S. Oishi, Accurate Sum and Dot Product, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.1955-1988, 2005.
DOI : 10.1137/030601818

M. L. Overton, Numerical Computing with IEEE Floating Point Arithmetic: Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises, Society for Industrial and Applied Mathematics, 2001.
DOI : 10.1137/1.9780898718072

D. M. Priest, On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations, 1992.

S. M. Rump, Ultimately Fast Accurate Summation, SIAM Journal on Scientific Computing, vol.31, issue.5, pp.3466-3502, 2009.
DOI : 10.1137/080738490

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.1673

S. M. Rump, Error estimation of floating-point summation and dot product, BIT Numerical Mathematics, vol.11, issue.3, pp.201-220, 2012.
DOI : 10.1007/s10543-011-0342-4

S. M. Rump, T. Ogita, and S. Oishi, Accurate Floating-Point Summation Part I: Faithful Rounding, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.189-224, 2008.
DOI : 10.1137/050645671

S. M. Rump, F. Bünger, and C. P. Jeannerod, Improved error bounds for floating-point products and Horner???s scheme, BIT Numerical Mathematics, vol.31, issue.1, 2015.
DOI : 10.1007/s10543-015-0555-z

URL : https://hal.archives-ouvertes.fr/hal-01137652

S. M. Rump and C. P. Jeannerod, Improved Backward Error Bounds for LU and Cholesky Factorizations, SIAM Journal on Matrix Analysis and Applications, vol.35, issue.2, pp.684-698, 2014.
DOI : 10.1137/130927231

URL : https://hal.archives-ouvertes.fr/hal-00841361

P. H. Sterbenz, Floating-Point Computation, 1974.

L. N. Trefethen, Computing numerically with functions instead of numbers, Communications of the ACM, vol.58, issue.10, pp.9-19, 2007.
DOI : 10.1145/2814847

J. H. Wilkinson, Error analysis of floating-point computation, Numerische Mathematik, vol.3, issue.1, pp.319-340, 1960.
DOI : 10.1007/BF01386233

J. H. Wilkinson, The Algebraic Eigenvalue Problem, 1965.