“…Therefore, new techniques have to be developed, that together with the usual preconditioned iterative methods can find approximate solutions in a faster way. Recently, Proper Orthogonal Decomposition (POD) methods (Markovinović and Jansen, 2006;Astrid et al, 2011;Pasetto et al, 2017;Diaz-Cortes et al, 2018) and deflation techniques (Vuik et al, 1999(Vuik et al, , 2002Diaz-Cortes et al, 2016) based on system information, have been studied to accelerate iterative methods for large and ill-conditioned problems. An extensive literature exists, with new and innovative ways of approaching deflation and POD methodologies.…”