Algebraic Adaptive Multipreconditioning applied to Restricted Additive Schwarz

In 2006 the Multi-Preconditioned Conjugate Gradient (MPCG) algorithm was introduced by Bridson and Greif [4]. It is an iterative linear solver, adapted from the Preconditioned Conjugate Gradient (PCG) algorithm which can be used in cases where several preconditioners are available or the usual preconditioner is a sum of contributions. In [4] it was already pointed out that Domain Decomposition algorithms are ideal candidates to benefit from MPCG.The question posed by this work is whether an adaptive MPCG algorithm can be developed for Restricted Additive Schwarz. The goal is to design an adaptive algorithm that is robust at a minimal cost. One great feature of Additive Schwarz is that it is algebraic (all the components in the preconditioner can be computed from the knowledge of matrix A) and we will aim to preserve this property