Selime Gürol

A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
  • Ehouarn Simon
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares Tags , ,

    The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation … Read more

    On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
  • Ehouarn Simon
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , ,

    This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm … Read more

    Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
    • Categories Nonlinear Systems and Least-Squares, Optimization of Simulated Systems, Optimization of Systems modeled by PDEs Tags , , , , ,

    When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each … Read more