关键词：Krylov子空间方法；剩余更换；数值稳定；迭代求解；稀疏矩阵
摘 要：Recent results have demonstrated the performance bene ts of communication- avoiding Krylov subspace methods, variants which use blocking strategies to perform O(s) com- putation steps of the algorithm for each communication step. This allows an O(s) reduction in total communication cost, which can lead to signi cant speedups on modern computer architectures. De- spite potential performance bene ts, stability of these variants has been an obstacle to their use in practice.