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，将其应用于基于轮廓积分的非线性特征值求解器，通过避免在每个积分节点计算代价高昂的矩阵分解，实现对线性系统的高效求解。我们采用多种技术使无限GMRES算法在实际应用中具备内存友好、计算高效和数值稳定的特性。具体而言，我们分析了多项式特征值问题与其缩放线性化形式之间的关系，并提出一种新颖的加权策略，能在该特定场景中显著加速无限GMRES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。通过理论分析和数值实验验证了所提算法的高效性。