A Recommendation System for Preconditioned Iterative Solvers

Abstract

Preconditioned iterative methods are often used to solve very large sparse systems of linear systems that arise in many scientific and engineering applications. The performance and robustness of these solvers is extremely sensitive to the choice of multiple preconditioner and solver parameters. Users of iterative methods often encounter an overwhelming number of combinations of choices for solvers, matrix preprocessing steps, preconditioners, and their parameters. The lack of a unified theoretical analysis of preconditioners coupled with limited knowledge of their interaction with linear systems makes it highly challenging for practitioners to choose good solver configurations. In this paper, we propose a novel, multi-stage learning based methodology for determining the best solver configurations to optimize the desired performance behavior for any given linear system. Empirical results over real performance data for the hyper iterative solver package demonstrate the efficacy and flexibility of the proposed approach.