A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in that it uses a closed-form expression for the augmented FOM approximants and hence circumvents the use of numerical quadrature. We further extend our method to use randomized sketching in order to avoid the arithmetic cost of orthogonalizing a full Krylov basis, offering an attractive solution to the fact that recycling algorithms built from shifted augmented FOM cannot easily be restarted. The efficacy of the proposed algorithms is demonstrated with numerical experiments.

翻译：本文提出一种面向矩阵函数序列高效计算的Krylov子空间循环再利用方法。该方法相较于[Burke等人，arXiv:2209.14163，2022]提出的循环技术，其改进在于采用增广FOM近似解的闭式表达式，从而避免了数值求积的使用。我们进一步将方法扩展至随机草图技术，以规避完整Krylov基正交化所需的高计算开销，从而为基于平移增广FOM的循环算法难以重启的问题提供具有吸引力的解决方案。通过数值实验验证了所提算法的有效性。