This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the complex-valued case is nontrivial and has been left as a conjecture. This paper establishes the connection between the convergence of the algorithm and the convexity of an objective function. Based on the connection, it demonstrates that when the sensing vectors are sampled uniformly from a unit sphere and the number of sensing vectors $m$ satisfies $m>O(n\log n)$ as $n, m\rightarrow\infty$, then this algorithm with a good initialization achieves linear convergence to the solution with high probability.

翻译：本文调查了随机的 Kaczmarz 算法对于相继检索复杂价值物体问题的趋同性。 虽然已经为实际估价案例研究了这一算法 }, 但该算法对复杂估价案例的概括性是非三重性的, 并留作一种猜测。 本文确定了算法趋同与客观函数的共性之间的联系。 基于此联系, 它表明当感应矢量从一个单位范围统一取样时, 当感应矢量从一个单位范围统一取样时, 且感应矢量为 $m>O(n\log n) 以$( $, m\\right\infty$) 满足时, 这个精准初始化的算法在极有可能的情况下实现了线性趋同解决方案的趋同性趋同性。