Jennifer Scott (STFC Rutherford Appleton Laboratory and The University of Reading, UK) & Jemima Tabeart (TU Eindhoven)
‘Sparsity: The key to tackling large-scale least squares problems’
Jennifer Scott
Linear least squares problems are a cornerstone of computational science and engineering. Over the years, the size of problems that researchers and practitioners face has constantly increased, making it essential that sparsity is exploited in the solution process. This talk presents a brief overview of modern numerical methods for tackling large least squares problems.
‘Numerical linear algebra for data assimilation’ Jemima Tabeart
The quality of a weather forecast is strongly determined by the accuracy of the initial condition. Data assimilation methods allow us to combine prior forecast information with new measurements in order to obtain the best estimate of the true initial condition. However, many of these approaches require the solution of an enormous least-squares problem. In this talk I will discuss some mathematical and computational challenges associated with data assimilation for numerical weather prediction, and show how structure-exploiting numerical linear algebra approaches can lead to theoretical and computational improvements. In particular I will show how re-writing the primal form of the weak-constraint 4D-Var problem as a saddle point formulation reveals the underlying block structure and hence admits a much richer class of preconditioners.
