Structured Sketching for Linear Systems

TL;DR

This paper introduces new iterative algorithms for solving linear systems using a sketch-and-project approach, which are memory-efficient and competitive with existing methods like GMRES and SYMMLQ.

Contribution

It develops weighted sketch-and-project algorithms with recursive formulas, improving efficiency and memory usage over traditional methods.

Findings

Algorithms perform well in numerical experiments

Comparable or better than GMRES and SYMMLQ

Low memory footprint and iteration complexity

Abstract

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.