, Maple PowerTool Interval Arithmetic

G. Gmp and . Multiple,

. Xsc-languages,

O. Aberth and M. J. Schaefer, Precise computation using range arithmetic, via C++, ACM TOMS, vol.18, issue.4, pp.481-491, 1992.

O. Aberth, Precise numerical methods using C++, 1998.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1964.

Y. Akyildiz, E. D. Popova, and C. P. Ullrich, Towards a more complete interval arithmetic in Mathematica, Proceedings of the Second International Mathematica Symposium, pp.29-36, 1997.

H. Brass, Quadraturverfahren. Vandenhoeck & Ruprecht, 1977.

H. Brass and K. Förster, On the application of the Peano representation of linear functionals in numerical analysis, Recent progress in inequalities, vol.430, pp.175-202, 1996.

R. P. Brent, A Fortran multiple-precision arithmetic package, ACM TOMS, vol.4, pp.57-70, 1978.

A. E. Connell and R. M. Corless, An experimental interval arithmetic package in Maple, Num. Analysis with Automatic Result Verification, 1993.

G. Corliss, intpak for Interval Arithmetic in Maple, Journal of Symbolic Computation, vol.11, 1994.

D. Daney, G. Hanrot, V. Lefèvre, F. Rouillier, and P. Zimmermann, The MPFR library, 2001.

I. Geulig, W. Krämer, and . Computeralgebra-und-verifikationsalgorithmen, , 1998.

I. Geulig and W. Krämer, Intervallrechnung in Maple -Die Erweiterung intpakX zum Paket intpak der Share-Library, 1999.

E. Hansen, Global optimization using interval analysis. Marcel Dekker, 1992.

E. Hansen and R. I. Greenberg, An interval Newton method, J. of Applied Math. and Computing, vol.12, pp.89-98, 1983.

T. Hickey, Q. Ju, and M. Van-emden, Interval arithmetic: from principles to implementation, J. of ACM, 2002.

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

R. B. Kearfott, Rigorous global search: continuous problems, 1996.

R. B. Kearfott and G. W. Walster, On stopping criteria in verified nonlinear systems or optimization algorithms, ACM TOMS, vol.26, issue.3, pp.373-389, 2000.

, J. Keiper. Interval arithmetic in Mathematica. Interval Computations, issue.3, 1993.

R. Klatte, U. Kulisch, C. Lawo, M. Rauch, and A. Wiethoff, C-XSC a C++ class library for extended scientific computing, 1993.

R. Klatte and U. Kulisch, , 1991.

O. Knueppel, PROFIL/BIAS -a fast interval library, Computing, vol.53, issue.3-4, pp.277-287, 1994.

W. Krämer, U. Kulisch, and R. Lohner, Numerical toolbox for verified computing II -Advanced Numerical Problems, 1998.

W. Krämer, Mehrfachgenaue reelle und intervallmässige Staggered-Correction Arithmetik mit zugehörigen Standardfunktionen, Report of the Institut für Angewandte Mathematik, Karlsruhe, 1988.

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

M. Lerch, G. Tischler, J. Wolff-von-gudenberg, W. Hofschuster, and W. Krämer, The interval library filib++ 2, vol.4, 2001.

N. N. Lebedev, Special functions and their applications, 1972.

R. Maeder, The Mathematica Programmer: Interval Plotting and Global Optimization, The Mathematica Journal, vol.7, issue.3, pp.279-290, 1999.

K. Petras, Numerical Computation of an Integral Representation for Arithmetic-Average Asian Options

K. Petras, A Method for Calculating the Complex Complementary Error Function with Prescribed Accuracy

L. B. , Automatic differentiation -Techniques and Applications, Lecture Notes in Computer Science, vol.120, 1981.

N. , Newton's algorithm using multiple precision interval arithmetic. To appear in Numerical Algorithms, Research report, vol.4334, 2001.

M. Grimmer, K. Petras, and N. ,

N. Revol and F. Rouillier, The MPFI library, 2001.
URL : https://hal.archives-ouvertes.fr/hal-02162346

N. Revol and F. Rouillier, Motivations for an arbitrary precision interval arithmetic and the MPFI library, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00100985

F. Rouillier and P. Zimmermann, Efficient isolation of polynomial real roots, J. of Computational and Applied Math, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072518

S. M. Rump, Solving algebraic problems with high accuraccy, A new approach to scientific computation. Proceedings of a symposium held at the IBM Research Center, pp.51-120, 1982.

S. Rump, Developments in reliable computing, T. Csendes ed., chapter INTLAB -Interval Laboratory, pp.77-104, 1999.

S. Rump, Fast and parallel interval arithmetic, BIT, vol.39, issue.3, pp.534-554, 1999.

M. Schröder, The Laplace transform approach to valuing exotic options: the case of the Asian option, Mathematical finance, pp.328-338, 2001.

, Sun Microsystems, Inc. C++ interval arithmetic programming reference, 2000.

J. M. Yohe, Portable software for interval arithmetic, Computing, pp.211-229, 1980.