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.

翻译：针对线性方程组 $Ax=b$，我们基于草图投影法开发了迭代算法。通过审慎选择草图（如残差历史记录），我们设计了能够实现简洁递归公式的加权策略。与常规草图投影法相比，所提算法具有较低的内存占用和迭代复杂度。在一系列数值实验中，新方法相较于GMRES、SYMMLQ以及前沿的随机求解器表现出优越性能。