Orthogonality and Biorthogonality: theory, numerical algorithms and applications Formal orthogonal polynomials with application to the construction of algorithms for implementing Lanczos--type methods for the solution of (possibly large) systems of linear equations.
Quasi--orthogonality for classical orthogonal polynomials with applications to quadrature (Gauss-Radau and Gauss-Lobatto formulas).
Acceleration of convergence and extrapolation methods
Theory and practice for acceleration and extrapolation methods. Application to the regularization of ill-conditioned linear systems and to their iterative solution (image restauration, medical imaging, ...) Application to algorithms for ranking the pages on the web (Google). Applications to Physics, Chemistry, Statistics, Economics, Biomathematics, ...