This paper considers the problem of detecting adjoint mismatch for two linear maps. To clarify, this means that we aim to calculate the operator norm for the difference of two linear maps, where for one we only have a black-box implementation for the evaluation of the map, and for the other we only have a black-box for the evaluation of the adjoint map. We give two stochastic algorithms for which we prove the almost sure convergence to the operator norm. The algorithm is a random search method for a generalization of the Rayleigh quotient and uses optimal step sizes. Additionally, a convergence analysis is done for the corresponding singular vector and the respective eigenvalue equation.

翻译：本文研究两个线性映射的伴随失配检测问题。具体而言，我们的目标是计算两个线性映射差值的算子范数，其中对于第一个映射仅掌握其正向计算的黑箱实现，而对于第二个映射仅掌握其伴随映射计算的黑箱实现。我们提出两种随机算法，并证明它们以概率1收敛到算子范数。该算法是对瑞利商广义形式的随机搜索方法，并采用最优步长。此外，我们对相应的奇异向量及对应的特征值方程进行了收敛性分析。