Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce quasi-optimal approximations over the Krylov subspace. Our numerical experiments outline the convergence of ROPMs for all matrices in our test set, with occasional spikes, but overall with a convergence rate similar to that of standard OPMs.

翻译：随机正交投影方法（ROPMs）可用于在不同场景下加速Krylov子空间方法的计算。通过理论分析与数值研究，我们证实这类方法能够在Krylov子空间上生成拟最优近似。数值实验表明，ROPMs对测试集中所有矩阵均呈现收敛性，尽管偶有波动，但整体收敛速率与标准正交投影方法（OPMs）相当。