`SLGMRES-E(mj, l, d)`

Goal: to implement the Adaptive SLGMRES-E, a hybrid method for improving GMRES(m) restraining the stagnation and slowdown convergence. The idea behind the variation of the structure of the GMRES(m) relies on the fact that once either the slowdown of convergence or stagnation is detected, a rule of switching between two strategies chooses the one most appropriate for facing the identified convergence problem. For this setup. two monotonically decreasing strategies, obtained from the literature, are combined: the LGMRES(m, l) and the GMRES-E(m, d) (which are already implemented and are part of the inspiration). This results in the switching method denoted as SLGMRES-E(m, d, l). In some cases, a proportional derivative rule is introduced to modify the restart parameter 'm', which gives place to this Adaptive SLGMRES-E(mj, d, l) algorithm.

For more information, the main article to be referred is the one by our colleague Cabral.