Research Interests

Sensitivity to the Cholesky factorization  Trainee report Initial vector of the Arnoldi process (work in progress) Homotopic perturbations F. Chaitin-Chatelin and E. Traviesas, Homotopic perturbation - Unfolding the field of singularities of a matrix by a complex parameter : a global geometric approach.  Tech. Rep. TR/PA/01/84, Postcript version, Pdf version, CERFACS.  F. Chaitin-Chatelin, V. Toumazou and E. Traviesas. Accuracy assessment for eigencomputations: Variety of backward errors and speudospectra. Journal Linear Algebra and its Applications, vol. 309, pp. 73-83.  Also available as CERFACS Technical Report TR/PA/99/03.   V. Toumazou and E. Traviesas. A note on homotopic backward error and pseudospectra for the generalized eigenproblem. Available as CERFACS Technical Report TR/PA/99/14. Hybrid eigensolver ISABeL A. N. Zaoui and E. Traviesas. The hybrid eigensolver ISABeL to compute the r eigenvalues closest to a given complex point: a qualitative study. Available as CERFACS technical Report TR/PA/00/13. To appear in the Proceedings of 16th IMACS World Congress, August 21-25, 2000, Lausanne, Switzerland. Special session on Hybrid Algorithms (S. Petiton organizer).   A. N. Zaoui and E. Traviesas. Sur la fiabilite et la robustesse du code ISABeL. Available as CERFACS Technical Report TR/PA/00/76. Krylov methods (Arnoldi method and GMRES Method) C. Mandry and E. Traviesas. Convergence de la méthode d'Arnoldi en précision finie en fonction du vecteur initial.  Working Note WN/PA/01/36 Keywords: Méthode d'Arnoldi, erreur inverse, défaut d'orthogonalité. Compressed PS, PDF  F. Chaitin-Chatelin, E. Traviesas and L. Plantie. Understanding Krylov methods in finite precision Available as CERFACS Technical Report TR/PA/00/40. To appear in the proceedings of the Second Conference on Numerical Analysis and Applications, June 11-15, 2000, Rousse, Bulgaria.   Loss of orthogonality and backward error analysis for Krylov based methods for linear systems and eigenproblems".(Trainee report in French Part 1 , Part 2 , Part 3.)   Backward error analysis of the Lanczos method applied to classical and generalized eigenproblem". Trainee report The Toolbox PRECISE F. Chaitin-Chatelin and E. Traviesas. PRECISE, a toolbox for assessing the quality of numerical methods and software.  Available as CERFACS technical Report TR/PA/00/12. To appear in the Proceedings of 16th IMACS World Congress, August 21-25, 2000, Lausanne, Switzerland. Special session on Recommender Systems (N. Ramakrishnan organizer). F. Chaitin-Chatelin and E. Traviesas. Finite Precision Computations and the toolbox PRECISE. Presented during the 2001 SIAM Meeting,  during the session on Accuracy and Reliability in Scientific Computing, July 9-13, 2001, San Diego.