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:随机正方位投影方法(ROPMs) 可用于加快不同情况下 Krylov 子空间方法的计算。 通过理论和数字调查, 我们确定这些方法会在 Krylov 子空间上产生准最佳近似值。 我们的数值实验勾勒了我们测试集中所有矩阵的ROPMs的趋同, 偶尔会发生峰值, 但总体的趋同率类似于标准OPMS 的趋同率 。