Randomized methods can be competitive for the solution of problems with a large matrix of low rank. They also have been applied successfully to the solution of large-scale linear discrete ill-posed problems by Tikhonov regularization (Xiang and Zou in Inverse Probl 29:085008, 2013). This entails the computation of an approximation of a partial singular value decomposition of a large matrix A that is of numerical low rank. The present paper compares a randomized method to a Krylov subspace method based on Golub–Kahan bidiagonalization with respect to accuracy and computing time and discusses characteristics of linear discrete ill-posed problems that make them well suited for solution by a randomized method.

随机方法对于解决大型低秩矩阵的问题可能具有竞争优势。它们也已通过Tikhonov正则化成功应用于大规模线性离散不适定问题的解决（Xiang和Zou in Inverse Probl 29：085008，2013）。这需要计算数值低秩的大矩阵A的部分奇异值分解的近似值。本文将随机方法与基于Golub–Kahan双对角化的Krylov子空间方法的准确性和计算时间进行了比较，并讨论了线性离散不适定问题的特征，这些问题使其非常适合通过随机方法求解。