Randomised preconditioning for variational data assimilation

  • Date:
  • Time: 14:00 - 15:30
  • Address:
    Sokolovská 83, Praha
  • Room: K3
  • Speaker: Ieva Daužickaitė

Data assimilation provides an improved estimate of a state of a dynamical system by combining a previous estimate with observations of the system. Large sparse linear systems of equations arise in a weak constraint four-dimensional variational data assimilation method. Iterative solvers are used, and preconditioning is essential to improve their performance. We consider four formulations of linear systems, particularly a symmetric positive definite (SPD) system arising in the so-called forcing formulation, and an SPD and two saddle point systems arising in the so-called state formulation; these exhibit different possibilities for parallel computations and sensitivities to the number of observations. Randomised methods for low-rank matrix approximations are used to construct suitable preconditioners for each system of equations. Numerical results with toy models show that the preconditioners can be effective.