Low rank preconditioner updates for sequences of linear systems arising from an optimal transport problem

In this work a class of tuned preconditioners is described in order to accelerate the Preconditioned Conjugate Gradient method applied to a sequence of linear systems, with symmetric positive definite coefficient matrices, arising from an Optimal Transport Problem. In particular low rank corrections for the Incomplete Cholesky initial preconditioners are experimented seeking out the efficient numerical solution. At this purpose, preconditioners of the Freitag-Spence class have been constructed and compared using different definitions for the corrective low rank matrix V, as the collection of solutions or the set of approximate eigenvectors arising from the Rayleigh-Ritz procedure. Numerical results of the proposed strategy are presented, preceeded by a preliminary study to identify the optimal parameters to work with. The numerical results show the effectiveness of this technique on the systems condition number and on reducing PCG iterations and overall CPU times