An approach recommender for preconditioned iterative solvers

Large sparse linear systems involving millions and even billions of equations are becoming in-creasingly common and direct solvers might not be a feasible option in certain cases due to their prohibitive computational and memory requirements. On the other hand, iterative solvers that require much lesser memory and possibly fewer computations than direct solvers, are often plagued by failure and or poor convergence. Decades of research [1] have culminated in the development of a wide range of iterative schemes and preconditioners that could easily leave a novice overwhelmed with the multitude of available options for solving a linear system. Fur-ther, determining the parameters required in the solution approach for general unsymmetric problems pose a challenging task even for an expert in computational linear algebra. Typically, fine-tuning the parameters can affect the performance of the preconditioned-solver with respect to time, memory, accuracy of the solution and also the number of iterations required while possibly improving the robustness of the approach. Depending on the choice of the precondi-tioner/solver, the parameter space could be really huge and an exhaustive search of this space for optimal parameters is non-trivial since some of the parameters could be continuous, discrete or a nested/linear combination of both. This suggests the need for a recommendation mode