Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new theoretical bounds on the performance of randomized block Krylov subspace methods for these problems. For matrices with polynomial spectral decay, the randomized block Krylov method can obtain an accurate spectral norm estimate using only a constant number of steps (that depends on the decay rate and the accuracy). Furthermore, the analysis reveals that the behavior of the algorithm depends in a delicate way on the block size. Numerical evidence confirms these predictions.

翻译：随机的块块 Krylov 亚空间方法形成了一种强大的算法类别,用于计算对称矩阵或总矩阵的极端单值的极端电子值。 本文的目的是为这些问题的随机块块块 Krylov 亚空间方法的性能制定新的理论界限。 对于多光谱衰减的矩阵,随机块块块 Krylov 方法只能使用固定数的步骤( 取决于衰减率和准确性) 获得准确的光谱规范估计。 此外, 分析表明, 算法的行为取决于块大小的微妙程度。 数字证据证实了这些预测。