In this paper, we introduce a randomized algorithm for solving the non-symmetric eigenvalue problem, referred to as randomized Implicitly Restarted Arnoldi (rIRA). This method relies on using a sketch-orthogonal basis during the Arnoldi process while maintaining the Arnoldi relation and exploiting a restarting scheme to focus on a specific part of the spectrum. We analyze this method and show that it retains useful properties of the Implicitly Restarted Arnoldi (IRA) method, such as restarting without adding errors to the Ritz pairs and implicitly applying polynomial filtering. Experiments are presented to validate the numerical efficiency of the proposed randomized eigenvalue solver.

翻译：本文提出了一种求解非对称特征值问题的随机化算法，称为随机隐式重启Arnoldi方法（rIRA）。该方法通过在Arnoldi过程中使用草图正交基，同时保持Arnoldi关系，并利用重启机制聚焦于谱的特定部分。我们分析了该方法，证明其保留了隐式重启Arnoldi方法（IRA）的有用性质，例如重启时不会向Ritz对引入误差，以及隐式应用多项式滤波。实验验证了所提出的随机特征值求解器的数值效率。