Structured Sketching for Linear Systems

For linear systems $Ax=b$ we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive formulas. The proposed algorithms have a low memory footprint and iteration complexity compared to regular sketch-and-project methods. In a set of numerical experiments the new methods compare well to GMRES, SYMMLQ and state-of-the-art randomized solvers.