In this work, the infinite GMRES algorithm, recently proposed by Correnty et al., is employed in contour integral-based nonlinear eigensolvers, avoiding the computation of costly factorizations at each quadrature node to solve the linear systems efficiently. Several techniques are applied to make the infinite GMRES memory-friendly, computationally efficient, and numerically stable in practice. More specifically, we analyze the relationship between polynomial eigenvalue problems and their scaled linearizations, and provide a novel weighting strategy which can significantly accelerate the convergence of infinite GMRES in this particular context. We also adopt the technique of TOAR to infinite GMRES to reduce the memory footprint. Theoretical analysis and numerical experiments are provided to illustrate the efficiency of the proposed algorithm.

翻译：本文采用Correnty等人近期提出的无限GMRES算法，用于基于等高线积分的非线性特征值求解器，通过避免在每个正交节点上计算昂贵的矩阵分解，高效求解线性系统。为使其在计算实践中兼具内存友好、高效与数值稳定性，本文应用了多种技术。具体而言，我们分析了多项式特征值问题与其缩放线性化之间的关系，并提出了一种新颖的加权策略，该策略能显著加速无限GMRES在此特定场景下的收敛速度。同时，我们将TOAR技术引入无限GMRES以降低内存占用。通过理论分析与数值实验，验证了所提算法的有效性。