This project aims at developing efficient and robust methods on high performance computers for solving large scale linear algebra problems. A quite wide spectrum of numerical methods is investigated. Direct solution methods for sparse systems of linear equations are at the core of the research interests in the team. Furthermore the development of efficient preconditioning techniques for the solution of very large systems of equations is also a topic currently addressed. We also develop research activities on numerical methods for eigenvalue problems.
Nonlinear systems and optimization
This project aims at developing efficient methods and codes for large-scale linear and nonlinear least squares, nonlinear systems, and nonlinear optimisation problems. Particular attention will be paid to linear and nonlinear parameter estimation and more specifically to data assimilation problems. These problems arise in various fields such as signal processing, geophysics, space dynamics, and meteorology. The algorithms used are based on very general results of probability and physics. However, what distinguishes the particular applications mentioned above is that they usually exhibit a strong structure that has to be exploited to obtain efficient algorithms. Our treatment use the recent advances made in least-squares solvers, to design fast and robust algorithms that might include: fast and robust parameter estimation, observability and sensitivity analysis, covariance estimation, regularization techniques for under-determined problems, design of efficient preconditioners, study of stopping criteria for iterative solvers.
More informations about this research topic are available on the dedicated Website.