This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions. We propose a stochastic method of random search type for the maximization of the Rayleigh quotient and employ an exact line search in the random search directions. Moreover, we show that the proposed algorithm converges to the global maximum (the operator norm) almost surely and illustrate the performance of the method with numerical experiments.

翻译：本文研究在仅能获取线性映射的评估值且存储条件受限的情况下，计算有限维希尔伯特空间之间线性映射的算子范数问题。我们提出一种随机搜索类型的随机方法，用于最大化瑞利商，并在随机搜索方向上进行精确线搜索。此外，我们证明所提算法几乎必然收敛于全局最大值（即算子范数），并通过数值实验展示了该方法的性能。