2004 F. Chaitin-Chatelin De la diversité des explications a l'unicité de la comprehension - Une approche mathematique. Prsentation au 16eme Colloque Interdisciplinaire de Carcassonne, Ecole d'Eté de l'Aude Juillet 2004, To appear. Pdf version .  F. Chaitin-Chatelin,  The dynamics of matrix coupling with an application to Krylov methods. Tech. Rep. TR/PA/04/29, Postcript version, Pdf version , CERFACS.  F. Chaitin-Chatelin,  and M. B. van Gijzen, Homotopic deviation with an application to computational acoustics. Tech. Rep. TR/PA/04/05, Postcript version, Pdf version, CERFACS.  Top of the page

2003 F. Chaitin-Chatelin , Computing beyond analyticity. Matrix algorithms in Inexact and Uncertain computing. Tech. Rep. TR/PA/03/110, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin , Elements of Hypercomputations on R and Z2 with the Dickson-Albert inductive process. Tech. Rep. TR/PA/03/34, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin , The Arnoldi method in the light of Homotopic Deviation theory. Tech. Rep. TR/PA/03/15, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin , On a recursive hierarchy for numbers algorithmically emerging from processing binary sequences. Tech. Rep. TR/PA/03/08, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin and M. B. van Gijzen, Homotopic deviation: an example in acoustics. Tech. Rep. TR/PA/03/04, Postcript version, Pdf version CERFACS.  Top of the page

2002 F. Chaitin-Chatelin , About Singularities in Inexact Computing. . Tech. Rep. TR/PA/02/106, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin and A. N. Zaoui, Hypercomputation on {0,1}. . Tech. Rep. TR/PA/02/73, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin and E. Traviesas, Qualitative Computing. in Handbook for Numerical Computation, SIAM. To appear. Tech. Rep. TR/PA/02/58, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin and E. Traviesas, PRECISE and the reliability of Numerical Software. in Handbook for Numerical Computation, SIAM. To appear. Tech. Rep. TR/PA/02/57, Postcript version, Pdf version CERFACS.  F. Chaitin-Chatelin, T. Meskauskas and M. van Gijzen,  Iterations emboitees pour la methode de la puissance avec acceleration de Tchebycheff en neurtronique. Contract Rep. CR/PA/02/56. CERFACS. F. Chaitin-Chatelin, T. Meskauskas, and A. N. Zaoui, Hypercomplex division in the presence of zero divisors on R and Z2. . Tech. Rep. TR/PA/02/29, Postcript version, Pdf version CERFACS.  Qualitative Computing Group Activity Report, 2000-2001. Postcript version  Top of the page

2001 F. Chaitin-Chatelin and T. Meskauskas, Computation with Hypercomplex Numbers, in Nonlinear Analysis 47, 3391-3400 Tech. Rep. TR/PA/00/69, CERFACS.    F. Chaitin-Chatelin, Hypercomplex Computation. 15th Householder Meeting. Abstract Postcript version Pdf version F. Chaitin-Chatelin and T. Meskauskas, Inner-Outer iterations for mode solvers in structural mechanics: application to the Code_Aster. Contract Report FR/PA/01/85.   F. Chaitin-Chatelin,  E. Traviesas, Homotopic perturbation: Unfolding the field of singularities of a matrix by a complex parameter. Tech. Rep. TR/PA/01/84, Postcript version, Pdf version, CERFACS.  Top of the page

2000 F. Chaitin-Chatelin, T. Meskauskas and A. N. Zaoui, About real and binary algebras: the interplay between geometry and algebra. Tech. Rep. TR/PA/00/74, CERFACS.   F. Chaitin-Chatelin,  E. Traviesas and L. Plantié, Understanding Krylov methods in finite precision. In Numerical Analysis and its Applications, NAA 2000 (L. Vulkov, J. Wasviewski, P. Yalamov eds), Springer Verlag, Lectures Notes in Computer Science, p. 187-197, 2000. Tech. Rep. TR/PA/00/40, CERFACS.   F. Chaitin-Chatelin,  E. Traviesas, PRECISE, a toolbox for assessing the quality of numerical methods and software. Proceedings of the 16th IMACS World Congress, Lausanne, Switzerland, 2000. Tech. Rep. TR/PA/00/12, CERFACS.   F. Chaitin-Chatelin, Comprendre les méthodes de Krylov en précision finie : le programme du Groupe Qualitative Computing au CERFACS. Tech. Rep. TR/PA/00/11, CERFACS.   F. Chaitin-Chatelin, The computing power of Geometry. Numerical Analysis 1999, D.F. Griffiths and G.A. Watson eds,  CRC Press LLC, pp. 83--92, 2000. Tech. Rep.TR/PA/99/24, CERFACS.   F. Chaitin-Chatelin, A. Harrabi and A. Ilahi, About Holder condition number and the stratification diagram for defective eigenvalues. Published in IMACS Journal on Mathematics and Computers in Simulation, dedicated to John Rice, (E.Houstis, R.Boisvert, and W.Dyksen eds), 54, pp. 397-402, 2000. Tech. Rep. TR/PA/99/19, CERFACS.   F. Chaitin-Chatelin, V. Toumazou and E. Traviesas, Accuracy assessment for eigencomputations : variety of backward errors and pseudospectra. Published in Linear Algebra and Appl.,309, pp 73--83, 2000. Tech. Rep. TR/PA/99/03. CERFACS.   F. Chaitin-Chatelin and S. Gratton,On the condition numbers associated with the polar factorization of a matrix. Tech. Rep. TR/PA/98/25 In Numerical Linear Algebra with Applications, 7, pp 337-354, 2000 Top of the page Top of the page

1999 F.Chaitin-Chatelin, Eléments d'une théorie naturelle de l'Information et de la Complexité, cours de DEA Ecole Doctorale Midi Pyrénées Sciences Economiques. F. Chaitin-Chatelin, Le Sens de la Vie, Tech. Rep. TR/PA/99/20 Postcript version, Pdf version, CERFACS. Top of the page

1998 F. Chaitin-Chatelin and A. Harrabi, About definitions of pseudospectra of closed operators in Banach spaces. Tech. Rep. TR/PA/98/08, CERFACS. Top of the page

1997 F. Chaitin-Chatelin, Is nonnormality a serious computational difficulty in practice?, in The quality of Numerical Software (R. F. Boisvert ed.), Chapmann and Hall, pp. 300--314. T. Braconnier and F. Chaitin-Chatelin, Roundoff induces a chaotic behaviour for eigensolvers applied on highly nonnormal matrices, in Computational Science for the 21st Century, (M. -O. Bristeau et al. eds), Wiley, 1997. Top of the page

1996  F. Chaitin-Chatelin, Is finite precision arithmetic useful for Physics ? in The finite, the bounded and the infinite, C. Calude ed., Proceedings of the Black Sea University, Journal UCS, vol. 2, pp. 380--395, 1996. F. Chaitin-Chatelin and S. Gratton, Convergence of successive iteration methods in finite precision under high nonnormality, in BIT, 36, pp.  455--469, 1996. Top of the page

1995 T. Braconnier, F. Chatelin and J.-C. Dunyach, Highly nonnormal eigenvalue problems in the aeronautical industry, in Japan J. Ind. Appl. Math., 12, pp. 123--136, 1995.  F. Chaitin-Chatelin, Le calcul qualitatif. Comment donner un sens à des resultats faux?, Tech. Rep. TR/PA/95/10, CERFACS. Report in french.   F. Chatelin, V. Frayssé and T. Braconnier, Computations in the neighbourhood of algebraic singularities, Numer. Funct. Anal. and Optimization,  16(3&4), 287--302, 1995. Top of the page

1994 F. Chatelin and T. Braconnier, About the qualitative computation of Jordan forms, ZAMM . Z. angew. Math. Mech. 74 (2), pp. 105--113, 1994.   F. Chatelin, Le calcul sur ordinateur à precision finie, Tech. Rep. TR/PA/94/05, CERFACS.