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）可用于加速多种场景下Krylov子空间方法的计算。通过理论与数值研究，我们证实这些方法能在Krylov子空间上产生拟最优逼近。数值实验表明，ROPMs对我们测试集中的所有矩阵均能收敛，虽偶有波动，但整体收敛速度与标准OPMs相近。