When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

We develop and analyze a broad family of stochastic/randomized algorithms for calculating
an approximate inverse matrix. We also develop specialized variants maintaining symmetry …

One of the key steps at each iteration of a randomized block coordinate descent method
consists in determining the update to a block of variables. Existing algorithms assume that in …

Variational data assimilation problems in meteorology and oceanography require the
solution of a regularized nonlinear least‐squares problem. Practical solution algorithms are …

Variational methods are widely used to solve geophysical inverse problems. Although
gradient‐based minimization algorithms are available for high‐dimensional problems …

In this article, we address the efficient numerical solution of linear and quadratic
programming problems, often of large scale. With this aim, we devise an infeasible interior …

Interior point methods (IPM) rely on the Newton method for solving systems of nonlinear
equations. Solving the linear systems which arise from this approach is the most …

We analyze and discuss matrix-free and limited memory preconditioners for sparse
symmetric positive definite systems and normal equations of large and sparse least-squares …

There is growing awareness that errors in the model equations cannot be ignored in data
assimilation methods such as four‐dimensional variational assimilation (4D‐Var). If allowed …

Correlation operators are used in the formulation of background‐error covariance models in
variational data assimilation (VDA) and for localizing low‐rank sample estimates of …