Data-Driven Solver and Preconditioner Selection for Sparse Linear Matrices

Solving large, sparse linear systems is at the core of diverse computational domains, where the efficient solution of such systems can heavily impact the total execution time of computations. While applying a preconditioner to an iterative solver has become standard, making optimal or sometimes even numerically stable choices can be quite challenging, mainly because the best combination depends strongly on the specific problem. We discuss how to predict effective preconditioner and iterative solver combinations for any given sparse linear system using a data-driven approach based on a combination of embedding and linear modeling techniques. We focus on determining useful system features and investigate different metrics to quantify the relative performance of the preconditioned solvers across matrices from the SuiteSparse collection.     «

Solving large, sparse linear systems is at the core of diverse computational domains, where the efficient solution of such systems can heavily impact the total execution time of computations. While applying a preconditioner to an iterative solver has become standard, making optimal or sometimes even numerically stable choices can be quite challenging, mainly because the best combination depends strongly on the specific problem. We discuss how to predict effective preconditioner and iterative sol...     »