M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

L. V. Ahlfors, Complex analysis. An introduction to the theory of analytic functions of one complex variable, 1979.

M. G. Arnold and S. Collange, A Real/Complex Logarithmic Number System ALU, IEEE Transactions on Computers, vol.60, issue.2, pp.202-213, 2011.
DOI : 10.1109/TC.2010.154

S. Banescu, F. De-dinechin, B. Pasca, and R. Tudoran, Multipliers for floating-point double precision and beyond on FPGAs, ACM SIGARCH Computer Architecture News, vol.38, issue.4, pp.73-79, 2011.
DOI : 10.1145/1926367.1926380

URL : https://hal.archives-ouvertes.fr/ensl-00475781

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

A. Benoit, M. Joldes, and M. Mezzarobba, Rigorous uniform approximation of D-finite functions, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01022420

A. Benoit and B. Salvy, Chebyshev expansions for solutions of linear differential equations, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.23-30, 2009.
DOI : 10.1145/1576702.1576709

URL : https://hal.archives-ouvertes.fr/inria-00395716

S. Bernstein, Leçons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d'une variable réelle professées à la Sorbonne, 1926.

Y. Bertot and P. Castéran, Interactive Theorem Proving and Program Development, Coq'Art:the Calculus of Inductive Constructions, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00344237

M. Berz and K. Makino, New methods for high-dimensional verified quadrature, Reliable Computing, vol.5, issue.1, pp.13-22, 1999.
DOI : 10.1023/A:1026437523641

M. Berz and K. Makino, Rigorous global search using taylor models, Proceedings of the 2009 conference on Symbolic numeric computation, SNC '09, pp.11-20, 2009.
DOI : 10.1145/1577190.1577198

M. Berz, K. Makino, and Y. Kim, Long-term stability of the tevatron by verified global optimization. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Proceedings of the 8th International Computational Accelerator Physics Conference -ICAP, pp.1-10, 2004.

W. G. Bickley, L. J. Comrie, J. C. Miller, D. H. Sadler, and A. J. Thompson, Bessel functions. Part II. Functions of positive integer order. British Association for the Advancement of Science, Mathematical Tables, p.186, 1952.

M. Blum, Program result checking: A new approach to making programs more reliable, Automata, Languages and Programming , 20th International Colloquium, ICALP93, Proceedings, pp.1-14, 1993.
DOI : 10.1007/3-540-56939-1_57

S. Boldo and . Lyon, Preuves formelles en arithmétiques à virgule flottante Available on the Web from http://www.ens-lyon.fr, 2004.

P. Borwein and T. Erdélyi, Polynomials and Polynomial Inequalities, Graduate Texts in Mathematics, vol.161, 1995.
DOI : 10.1007/978-1-4612-0793-1

A. Bostan, B. Salvy, and E. Schost, Power series composition and change of basis, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, pp.269-276, 2008.
DOI : 10.1145/1390768.1390806

URL : https://hal.archives-ouvertes.fr/inria-00273385

A. Bostan, B. Salvy, and E. Schost, Fast conversion algorithms for orthogonal polynomials, Linear Algebra and its Applications, vol.432, issue.1, pp.249-258, 2010.
DOI : 10.1016/j.laa.2009.08.002

URL : https://hal.archives-ouvertes.fr/inria-00273508

R. J. Boulton, Efficiency in a fully-expansive theorem prover, 1993.

J. P. Boyd, Chebyshev and Fourier spectral methods, 2001.
DOI : 10.1007/978-3-642-83876-7

R. P. Brent and H. T. Kung, O((n log n)3/2) ALGORITHMS FOR COMPOSITION AND REVERSION OF POWER SERIES, Analytic Computational Complexity, pp.217-225, 1975.
DOI : 10.1016/B978-0-12-697560-4.50018-6

R. P. Brent and H. T. Kung, Fast Algorithms for Manipulating Formal Power Series, Journal of the ACM, vol.25, issue.4, pp.581-595, 1978.
DOI : 10.1145/322092.322099

N. Brisebarre and S. Chevillard, Efficient polynomial L-approximations, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), pp.169-176, 2007.
DOI : 10.1109/ARITH.2007.17

URL : https://hal.archives-ouvertes.fr/inria-00119513

N. Brisebarre and M. Joldes, Chebyshev interpolation polynomial-based tools for rigorous computing, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pp.147-154, 2010.
DOI : 10.1145/1837934.1837966

URL : https://hal.archives-ouvertes.fr/ensl-00472509

N. Brisebarre, J. Muller, and A. Tisserand, Computing machine-efficient polynomial approximations, ACM Transactions on Mathematical Software, vol.32, issue.2, pp.236-256, 2006.
DOI : 10.1145/1141885.1141890

URL : https://hal.archives-ouvertes.fr/ensl-00086826

M. Bronstein, Symbolic integration. I, volume 1 of Algorithms and Computation in Mathematics, 2005.

M. Bronstein and B. Salvy, Full partial fraction decomposition of rational functions, Proceedings of the 1993 international symposium on Symbolic and algebraic computation , ISSAC '93, pp.157-160, 1993.
DOI : 10.1145/164081.164114

L. Brutman, Lebesgue functions for polynomial interpolation?a survey The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T, Ann. Numer. Math. J. Rivlin, vol.414, pp.111-127, 1997.

C. Chen, Computing interval enclosures for definite integrals by application of triple adaptive strategies, Computing, pp.81-99, 2006.

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

R. C. Cheung, D. Lee, W. Luk, and J. D. Villasenor, Hardware Generation of Arbitrary Random Number Distributions From Uniform Distributions Via the Inversion Method, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, pp.952-962, 2007.
DOI : 10.1109/TVLSI.2007.900748

S. Chevillard, Évaluation efficace de fonctions numériques. Outils et exemples, 2009.

S. Chevillard, J. Harrison, M. Jolde¸sjolde¸s, and C. Lauter, 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

S. Chevillard, M. Jolde¸sjolde¸s, and C. Lauter, Sollya: An Environment for the Development of Numerical Codes, Mathematical Software -ICMS 2010, pp.28-31, 2010.
DOI : 10.1007/978-3-642-15582-6_5

URL : https://hal.archives-ouvertes.fr/hal-00761644

S. Chevillard, M. Joldes, and C. Lauter, Certified and Fast Computation of Supremum Norms of Approximation Errors, 2009 19th IEEE Symposium on Computer Arithmetic, pp.169-176, 2009.
DOI : 10.1109/ARITH.2009.18

URL : https://hal.archives-ouvertes.fr/ensl-00334545

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

S. Chevillard, . Ch, M. Lauter, and . Joldes, Users' manual for the Sollya tool, Release 2.0. https, 2010.

F. Cháves and M. Daumas, A library of taylor models for pvs automatic proof checker, Proceedings of the NSF workshop on reliable engineering computing, pp.39-52, 2006.

C. W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proceedings of the Cambridge Philosophical Society, pp.134-149, 1957.
DOI : 10.1017/S0305004100032072

G. F. Corliss, Survey of interval algorithms for ordinary differential equations, Special Issue Numerical Ordinary Diferrential Equations (Proceedings of the 1986 ODE Conference, pp.112-120, 1989.
DOI : 10.1016/0096-3003(89)90112-4

G. F. Corliss, Guaranteed error bounds for ordinary differential equations, Theory of Numerics in Ordinary and Partial Differential Equations, pp.1-75, 1994.

F. De-dinechin, M. Joldes, and B. Pasca, Automatic generation of polynomial-based hardware architectures for function evaluation, ASAP 2010, 21st IEEE International Conference on Application-specific Systems, Architectures and Processors, pp.216-222, 2010.
DOI : 10.1109/ASAP.2010.5540952

URL : https://hal.archives-ouvertes.fr/ensl-00470506

F. De-dinechin, C. Klein, and B. Pasca, Generating high-performance custom floating-point pipelines, 2009 International Conference on Field Programmable Logic and Applications, pp.2009-2025, 2009.
DOI : 10.1109/FPL.2009.5272553

URL : https://hal.archives-ouvertes.fr/ensl-00379154

F. De-dinechin, C. Q. Lauter, and G. Melquiond, Assisted verification of elementary functions using Gappa, Proceedings of the 2006 ACM symposium on Applied computing , SAC '06, pp.1318-1322, 2006.
DOI : 10.1145/1141277.1141584

F. De-dinechin and B. Pasca, Large multipliers with fewer DSP blocks, 2009 International Conference on Field Programmable Logic and Applications, 2009.
DOI : 10.1109/FPL.2009.5272296

F. De-dinechin and A. Tisserand, Multipartite table methods, IEEE Transactions on Computers, vol.54, issue.3, pp.319-330, 2005.
DOI : 10.1109/TC.2005.54

URL : https://hal.archives-ouvertes.fr/ensl-00542210

J. Detrey and F. De-dinechin, Table-based polynomials for fast hardware function evaluation, 2005 IEEE International Conference on Application-Specific Systems, Architecture Processors (ASAP'05), pp.328-333, 2005.
DOI : 10.1109/ASAP.2005.61

J. Detrey and F. De-dinechin, Floating-Point Trigonometric Functions for FPGAs, 2007 International Conference on Field Programmable Logic and Applications, pp.29-34, 2007.
DOI : 10.1109/FPL.2007.4380621

J. Detrey and F. De-dinechin, Parameterized floating-point logarithm and exponential functions for FPGAs. Microprocessors and Microsystems, Special Issue on FPGA-based Reconfigurable Computing, pp.31537-545, 2007.
URL : https://hal.archives-ouvertes.fr/ensl-00542213

T. A. Driscoll, F. Bornemann, and L. N. Trefethen, The chebop system for automatic solution of differential equations, BIT Numerical Mathematics, vol.1, issue.4, pp.701-723, 2008.
DOI : 10.1007/s10543-008-0198-4

I. Eble and M. Neher, ACETAF, ACM Transactions on Mathematical Software, vol.29, issue.3, pp.263-286, 2003.
DOI : 10.1145/838250.838252

H. Ehlich and K. Zeller, Schwankung von Polynomen zwischen Gitterpunkten, Mathematische Zeitschrift, vol.3, issue.1, pp.41-44, 1964.
DOI : 10.1007/BF01111276

T. H. Einwohner and R. J. Fateman, A MACSYMA package for the generation and manipulation of chebyshev series, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation , ISSAC '89, pp.180-185, 1989.
DOI : 10.1145/74540.74562

M. K. El-daou, E. L. Ortiz, and H. Samara, A unified approach to the Tau Method and Chebyshev series expansion techniques, Computers & Mathematics with Applications, vol.25, issue.3, pp.73-82, 1993.
DOI : 10.1016/0898-1221(93)90145-L

D. Elliott, D. F. Paget, G. M. Phillips, and P. J. Taylor, Error of truncated Chebyshev series and other near minimax polynomial approximations, Journal of Approximation Theory, vol.50, issue.1, pp.49-57, 1987.
DOI : 10.1016/0021-9045(87)90065-7

C. Epstein, W. L. Miranker, and T. J. Rivlin, Ultra-arithmetic I: Function data types, Mathematics and Computers in Simulation, vol.24, issue.1, pp.1-18, 1982.
DOI : 10.1016/0378-4754(82)90045-3

C. Epstein, W. L. Miranker, and T. J. Rivlin, Ultra-arithmetic II: intervals of polynomials, Mathematics and Computers in Simulation, vol.24, issue.1, pp.19-29, 1982.
DOI : 10.1016/0378-4754(82)90046-5

L. Fousse, Intégration numérique avec erreur bornée en précision arbitraire, PhD in Computer Science, 2006.

L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, MPFR, ACM Transactions on Mathematical Software, vol.33, issue.2, 2007.
DOI : 10.1145/1236463.1236468

URL : https://hal.archives-ouvertes.fr/inria-00070266

L. Fox, Chebyshev Methods for Ordinary Differential Equations, The Computer Journal, vol.4, issue.4, p.318, 1962.
DOI : 10.1093/comjnl/4.4.318

L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, 1968.

W. Gautschi, Computational Aspects of Three-Term Recurrence Relations, SIAM Review, vol.9, issue.1, pp.24-82, 1967.
DOI : 10.1137/1009002

W. Gautschi, Questions of numerical condition related to polynomials Studies in Numerical Analysis, MAA Stud, Math., Math. Assoc. America, issue.24, pp.140-177, 1984.

K. O. Geddes, Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's, Proceedings of the 1977 MACSYMA User's Conference, pp.405-423, 1977.

P. Giorgi, On Polynomial Multiplication in Chebyshev Basis, IEEE Transactions on Computers, vol.61, issue.6, 2010.
DOI : 10.1109/TC.2011.110

URL : https://hal.archives-ouvertes.fr/hal-00520207

X. Gourdon, Combinatoire, Algorithmique et Géometrie des Polynômes, 1996.

X. Gourdon and B. Salvy, Effective asymptotics of linear recurrences with rational coefficients, Discrete Mathematics, vol.153, issue.1-3, pp.145-163, 1996.
DOI : 10.1016/0012-365X(95)00133-H

A. Griewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Number 19 in Frontiers in Appl, Math. SIAM, 2000.
DOI : 10.1137/1.9780898717761

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

. C. Th and . Hales, The flyspeck project

E. Hansen, AN OVERVIEW OF GLOBAL OPTIMIZATION USING INTERVAL ANALYSIS, 1992.
DOI : 10.1016/B978-0-12-505630-4.50021-3

J. Harrison, Floating point verification in HOL light: The exponential function, 1997.
DOI : 10.1007/BFb0000475

J. Harrison, Formal Verification of Floating Point Trigonometric Functions, Formal Methods in Computer-Aided Design: Third International Conference FMCAD 2000, pp.217-233, 1954.
DOI : 10.1007/3-540-40922-X_14

J. Harrison, Verifying Nonlinear Real Formulas Via Sums of Squares, Proc. 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

C. Jacobi, Formal Verification of a Fully IEEE Compliant Floating Point Unit Available on the Web as http, 2002.

R. Kaivola and M. D. Aagaard, Divider Circuit Verification with Model Checking and Theorem Proving, Theorem Proving in Higher Order Logics: 13th International Conference, pp.338-355, 2000.
DOI : 10.1007/3-540-44659-1_21

E. W. Kaucher and W. L. Miranker, Self-validating numerics for function space problems, 1984.

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

P. Kirchberger, Über Tchebychefsche Annäherungsmethoden, 1902.
DOI : 10.1007/bf01445182

D. Knuth, The Art of Computer Programming: Seminumerical Algorithms, 1997.

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

C. Lanczos, Trigonometric Interpolation of Empirical and Analytical Functions, Journal of Mathematics and Physics, vol.XX, issue.1-4, pp.123-199, 1938.
DOI : 10.1002/sapm1938171123

C. Lauter and F. De-dinechin, Optimising polynomials for floating-point implementation, Proceedings of the 8th Conference on Real Numbers and Computers, pp.7-16, 0190.

D. Lee, J. D. Villasenor, W. Luk, and P. H. Leong, A hardware Gaussian noise generator using the Box-Muller method and its error analysis, IEEE Transactions on Computers, vol.55, issue.6, p.55, 2006.
DOI : 10.1109/TC.2006.81

D. U. Lee, A. A. Gaffar, O. Mencer, and W. Luk, Optimizing Hardware Function Evaluation, IEEE Transactions on Computers, vol.54, issue.12, pp.1520-1531, 2005.
DOI : 10.1109/TC.2005.201

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, 2001.
DOI : 10.1109/ARITH.2001.930110

S. Lewanowicz, Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series, Zastosowania Matematyki, XV, issue.3, pp.345-395, 1976.

S. Lewanowicz, A new approach to the problem of constructing recurrence relations for the jacobi coefficients, Zastos. Mat, vol.21, pp.303-326, 1991.

K. Makino, Rigorous Analysis of Nonlinear Motion in Particle Accelerators, 1998.

K. Makino and M. Berz, Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, vol.4, issue.4, pp.379-456, 2003.

K. Makino and M. Berz, Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, vol.4, issue.4, pp.379-456, 2003.

K. Makino and M. Berz, Rigorous integration of flows and ODEs using taylor models, Proceedings of the 2009 conference on Symbolic numeric computation, SNC '09, pp.79-84, 2009.
DOI : 10.1145/1577190.1577206

P. Markstein, IA-64 and Elementary Functions : Speed and Precision. Hewlett-Packard Professional Books, 2000.

J. C. Mason and D. C. Handscomb, Chebyshev polynomials, 2003.
DOI : 10.1201/9781420036114

R. J. Mathar, Chebyshev series expansion of inverse polynomials, Journal of Computational and Applied Mathematics, vol.196, issue.2, pp.596-607, 2006.
DOI : 10.1016/j.cam.2005.10.013

K. Mehlhorn, S. Nher, M. Seel, R. Seidel, . Th et al., Checking geometric programs or verification of geometric structures, Proceedings of the 12th Annual Symposium on Computational Geometry (FCRC'96), pp.159-165, 1996.

G. Melquiond, Floating-point arithmetic in the Coq system, Proc. 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

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

M. Mezzarobba, NumGfun, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pp.139-146, 2010.
DOI : 10.1145/1837934.1837965

URL : https://hal.archives-ouvertes.fr/inria-00456983

M. Mezzarobba and B. Salvy, Effective bounds for P-recursive sequences, Journal of Symbolic Computation, vol.45, issue.10, pp.1075-1096, 2010.
DOI : 10.1016/j.jsc.2010.06.024

URL : https://hal.archives-ouvertes.fr/inria-00376219

P. Molin, Intégration numérique et calculs de fonctions L, 2010.

J. Strother-moore, T. Lynch, and M. Kaufmann, A mechanically checked proof of the AMD5/sub K/86/sup TM/ floating-point division program, IEEE Transactions on Computers, vol.47, issue.9, pp.913-926, 1998.
DOI : 10.1109/12.713311

R. E. Moore, Interval Arithmetic and Automatic Error Analysis in Digital Computing, 1962.

R. E. Moore, Interval Analysis, 1966.

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

R. E. Moore, R. B. Kearfott, and M. J. Cloud, Introduction to interval analysis, SIAM, 2009.
DOI : 10.1137/1.9780898717716

J. Muller, Projet ANR TaMaDi ? dilemme du fabricant de tables ? table maker's dilemma (ref. ANR, 2010.

J. Muller, Elementary Functions, Algorithms and Implementation, 2006.
URL : https://hal.archives-ouvertes.fr/ensl-00000008

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

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

J. Muller, N. Brisebarre, F. De-dinechin, C. Jeannerod, V. Lefèvre et al., Handbook of Floating-Point Arithmetic, 2009.
DOI : 10.1007/978-0-8176-4705-6

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

N. Th and . Müller, The iRRAM: Exact arithmetic in c++

P. S. Nataraj and K. Kotecha, Global Optimization with Higher Order Inclusion Function Forms Part 1: A Combined Taylor-Bernstein Form, Reliable Computing, vol.10, issue.1, pp.27-44, 2004.
DOI : 10.1023/B:REOM.0000003995.08805.2a

N. S. Nedialkov, K. R. Jackson, and G. F. Corliss, Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation, vol.105, issue.1, pp.21-68, 1999.
DOI : 10.1016/S0096-3003(98)10083-8

M. Neher, K. R. Jackson, and N. S. Nedialkov, On Taylor Model Based Integration of ODEs, SIAM Journal on Numerical Analysis, vol.45, issue.1, pp.236-262, 2007.
DOI : 10.1137/050638448

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

J. O. Leary, X. Zhao, R. Gerth, and C. H. Seger, Formally verifying IEEE compliance of floating-point hardware Available on the Web as http, Intel Technology Journal, pp.1-14, 1999.

R. Pachón and L. N. Trefethen, Barycentric-Remez algorithms for best polynomial approximation in the chebfun system, BIT Numerical Mathematics, vol.2, issue.3, pp.721-741, 2009.
DOI : 10.1007/s10543-009-0240-1

V. Y. Pan, Optimal and nearly optimal algorithms for approximating polynomial zeros, Computers & Mathematics with Applications, vol.31, issue.12, pp.97-138, 1996.
DOI : 10.1016/0898-1221(96)00080-6

URL : http://doi.org/10.1016/0898-1221(96)00080-6

V. Y. Pan, New fast algorithms for polynomial interpolation and evaluation on the Chebyshev node set, Computers & Mathematics with Applications, vol.35, issue.3, pp.125-129, 1998.
DOI : 10.1016/S0898-1221(97)00283-6

P. A. Parrilo, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, pp.293-320, 2003.
DOI : 10.1007/s10107-003-0387-5

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.3194

S. Paszkowski, Zastosowania numeryczne wielomianow i szeregow Czebyszewa. Podstawowe Algorytmy Numeryczne, 1975.

R. B. Platte and L. N. Trefethen, Chebfun: A New Kind of Numerical Computing, Progress in Industrial Mathematics at ECMI 2008, pp.69-87, 2010.
DOI : 10.1007/978-3-642-12110-4_5

M. J. Powell, On the Maximum Errors of Polynomial Approximations Defined by Interpolation and by Least Squares Criteria, The Computer Journal, vol.9, issue.4, pp.404-407, 1967.
DOI : 10.1093/comjnl/9.4.404

M. J. Powell, Approximation theory and methods, 1981.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1992.

H. Ratschek and J. Rokne, New computer methods for global optimization, 1988.

L. Rebillard, Etude théorique et algorithmique des series de Chebychev, solutions d'équations différentielles holonomes, 1998.

N. Revol and F. Rouillier, The MPFI library
URL : https://hal.archives-ouvertes.fr/inria-00544998

T. J. Rivlin, Chebyshev polynomials. From approximation theory to algebra. Pure and Applied Mathematics, 1990.

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

M. Roy, Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals, of Expositions in Mathematics. de Gruyter Lectures in Real Geometry, 1996.
DOI : 10.1515/9783110811117.1

S. Rump, Fast and parallel interval arithmetic, Bit Numerical Mathematics, vol.39, issue.3, pp.534-554, 1999.
DOI : 10.1023/A:1022374804152

S. M. Rump, Algorithms for verified inclusion, Reliability in Computing, Perspectives in Computing, pp.109-126, 1988.

D. Russinoff, Abstract, LMS Journal of Computation and Mathematics, vol.11, pp.148-200, 1998.
DOI : 10.1112/S1461157000000176

B. Salvy, D-finiteness, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.2-3, 2005.
DOI : 10.1145/1073884.1073886

B. Salvy and P. Zimmermann, GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software, vol.20, issue.2, pp.163-177, 1994.
DOI : 10.1145/178365.178368

URL : https://hal.archives-ouvertes.fr/hal-00917741

M. Schatzman, Numerical Analysis, A Mathematical Introduction, 2002.

V. Stahl, Interval Methods for Bounding the Range of Polynomials and Solving Systems of Nonlinear Equations, 1995.

R. P. Stanley, Differentiably Finite Power Series, European Journal of Combinatorics, vol.1, issue.2, pp.175-188, 1980.
DOI : 10.1016/S0195-6698(80)80051-5

T. Sunaga, Theory of interval algebra and its application to numerical analysis. RAAG Memoirs, Ggujutsu Bunken Fukuy-kai, pp.29-46, 1958.

D. A. Sunderland, R. A. Strauch, S. S. Wharfield, H. T. Peterson, C. +r et al., CMOS/SOS frequency synthesizer LSI circuit for spread spectrum communications, IEEE Journal of Solid-State Circuits, vol.19, issue.4, pp.497-506, 1984.
DOI : 10.1109/JSSC.1984.1052173

A. Tisserand, High-performance hardware operators for polynomial evaluation, International Journal of High Performance Systems Architecture, vol.1, issue.1, pp.14-23, 2007.
DOI : 10.1504/IJHPSA.2007.013288

URL : https://hal.archives-ouvertes.fr/lirmm-00140930

L. N. Trefethen, Approximation Theory and Approximation Practice, Draft version, 2011.

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

L. N. Trefethen, Chebfun Version 4.0. The Chebfun Development Team, 2011.

W. Tucker, A Rigorous ODE Solver and Smale???s 14th Problem, Foundations of Computational Mathematics, vol.2, issue.1, pp.53-117, 2002.
DOI : 10.1007/s002080010018

W. Tucker, Auto-validating numerical methods, 2009.

J. Van-der-hoeven, Making fast multiplication of polynomials numerically stable, 2008.

L. Veidinger, On the numerical determination of the best approximations in the Chebyshev sense, Numerische Mathematik, vol.13, issue.No. 67, pp.99-105, 1960.
DOI : 10.1007/BF01386215

J. Zur-gathen and J. Gerhard, Modern computer algebra, 2003.
DOI : 10.1017/CBO9781139856065

F. Wiedijk, The seventeen provers of the world, Lecture Notes in Computer Science, vol.3600, 2006.
DOI : 10.1007/11542384

J. Wimp, Computation with Recurrence Relations, 1984.

K. E. Wires, M. J. Schulte, and D. Mccarley, FPGA Resource Reduction Through Truncated Multiplication, International Conference on Field Programmable Logic and Applications, pp.574-583, 2001.
DOI : 10.1007/3-540-44687-7_59

S. Wolfram, The Mathematica Book. Wolfram Media, Incorporated, 0194.

R. C. Young, The algebra of many-valued quantities, Mathematische Annalen, vol.17, issue.5, pp.260-290, 1931.
DOI : 10.1007/BF01457934

R. V. Zahar, A mathematical analysis of Miller's algorithm, Numerische Mathematik, vol.26, issue.4, pp.427-447, 1976.
DOI : 10.1007/BF01399606

D. Zeilberger, A holonomic systems approach to special functions identities, Journal of Computational and Applied Mathematics, vol.32, issue.3, pp.321-368, 1990.
DOI : 10.1016/0377-0427(90)90042-X

A. Ziv, 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

R. Zumkeller, Formal Global Optimization with Taylor Models, Proc. of the 4th International Joint Conference on Automated Reasoning, pp.408-422, 2008.

R. Zumkeller, Global Optimization in Type Theory, 2008.