R. Yates, Fixed-Point Arithmetic: An Introduction, Digital Signal Labs, 2013.

D. Menard, D. Chillet, and O. Sentieys, Floating-to-Fixed-Point Conversion for Digital Signal Processors, EURASIP Journal on Applied Signal Processing, vol.37, issue.8, pp.1-15, 2006.
DOI : 10.1155/ASP/2006/96421

URL : https://hal.archives-ouvertes.fr/inria-00459212

Z. Nikolic, H. T. Nguyen, and G. Frantz, Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs, EURASIP Journal on Advances in Signal Processing, vol.2007, issue.1, 2007.
DOI : 10.1109/29.45619

W. Sung and K. Kum, Simulation-based word-length optimization method for fixed-point digital signal processing systems, IEEE Transactions on Signal Processing, vol.43, issue.12, pp.3087-3090, 1995.
DOI : 10.1109/78.476465

D. Lee, A. A. Gaffar, R. C. Cheung, O. Mencer, W. Luk et al., Accuracy-Guaranteed Bit-Width Optimization, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.25, issue.10, 1990.
DOI : 10.1109/TCAD.2006.873887

C. F. Fang, R. A. Rutenbar, T. Chen, and F. , Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs, ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486), pp.275-282, 2003.
DOI : 10.1109/ICCAD.2003.159701

G. Golub and I. Mitchell, Matrix factorizations in Fixed Point on the C6x VLIW architecture, 1998.

M. Mehlhose and S. Schiffermüller, Efficient Fixed-Point Implementation of Linear Equalization for Cooperative MIMO Systems, 17th European Signal Processing Conference, 2009.

A. Irturk, B. Benson, S. Mirzaei, and R. Kastner, GUSTO, ACM Transactions on Embedded Computing Systems, vol.9, issue.4, pp.1-32, 2010.
DOI : 10.1145/1721695.1721698

A. Y. Syed, M. Qasim, and A. Ahmed, Telba, FPGA Design and Implementation of Matrix Multiplier Architectures for Image and Signal Processing Applications, International Journal of Computer Science and Network Security, vol.10, issue.2, pp.168-176, 2010.

I. Sotiropoulos and I. Papaefstathiou, A fast parallel matrix multiplication reconfigurable unit utilized in face recognitions systems, 2009 International Conference on Field Programmable Logic and Applications, pp.276-281, 2009.
DOI : 10.1109/FPL.2009.5272287

S. J. Campbell and S. P. Khatri, Resource and delay efficient matrix multiplication using newer FPGA devices, Proceedings of the 16th ACM Great Lakes symposium on VLSI , GLSVLSI '06, pp.308-311, 2006.
DOI : 10.1145/1127908.1127979

C. Mouilleron and G. Revy, Automatic Generation of Fast and Certified Code for Polynomial Evaluation, 2011 IEEE 20th Symposium on Computer Arithmetic, pp.95-103, 2011.
DOI : 10.1109/ARITH.2011.39

URL : https://hal.archives-ouvertes.fr/ensl-00531721

M. A. Najahi, Synthesis of certified programs in fixed-point arithmetic, and its application to linear algebra basic blocks, 2014.
URL : https://hal.archives-ouvertes.fr/lirmm-01277374

B. Lopez, T. Hilaire, and L. Didier, Sum-of-products evaluation schemes with fixed-point arithmetic, and their application to IIR filter implementation, Proc. of the Conference on Design and Architectures for Signal and Image Processing, pp.2012-160
URL : https://hal.archives-ouvertes.fr/hal-01076043

R. E. Moore, Interval Analysis, 1966.

E. Hansen, A generalized interval arithmetic, Interval Mathematics, pp.7-18, 1975.
DOI : 10.1007/3-540-07170-9_2

M. D. Ercegovac, L. Imbert, D. W. Matula, J. Muller, and G. Wei, Improving Goldschmidt division, square root, and square root reciprocal, IEEE Transactions on Computers, vol.49, issue.7, pp.759-763, 2000.
DOI : 10.1109/12.863046

URL : https://hal.archives-ouvertes.fr/inria-00072909

N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2002.
DOI : 10.1137/1.9780898718027

S. Kim, K. Kum, and W. Sung, Fixed-point optimization utility for c and c++ based digital signal processing programs, IEEE Trans. Circuits and Systems II, pp.1455-1464, 1996.

M. Martel, A. Najahi, and G. Revy, Code Size and Accuracy-Aware Synthesis of Fixed-Point Programs for Matrix Multiplication, Proc. of the 4th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS'14), pp.204-214, 2014.
URL : https://hal.archives-ouvertes.fr/lirmm-00860383

D. Lee and J. D. Villasenor, Optimized Custom Precision Function Evaluation for Embedded Processors, IEEE Transactions on Computers, vol.58, issue.1, pp.46-59, 2009.
DOI : 10.1109/TC.2008.124

M. I. Shamos and D. Hoey, Closest-point problems, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975), pp.151-162, 1975.
DOI : 10.1109/SFCS.1975.8

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (3, 2009.

C. Mouilleron, Efficient computation with structured matrices and arithmetic expressions, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00688388

L. Zhou, L. Qiu, and J. Zhu, A novel adaptive equalization algorithm for MIMO communication system, Proc. of the IEEE 62nd Vehicular Technology Conference (VTC-2005-Fall), pp.2408-2412, 2005.

H. Chen, X. Deng, and A. Haimovich, Layered turbo space-time coded mimoofdm systems for time varying channels, Proc. of the 2003 IEEE Global Telecommunications Conference (GLOBECOM'03), pp.1831-183610, 2003.

J. R. Guerci, Space-time adaptive processing for radar, 2003.