A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov space. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing.

翻译：提出了一种草选Arnoldi过程，用于以低成本生成Krylov空间的良态基。在每个迭代步中，该方法利用随机化草图技术选择少量先前计算得到的基向量，并从当前基向量中投影去除这些分量。计算成本随Krylov空间维度线性增长。针对投影步骤中的子集选择问题，采用统计学习与压缩感知中多种启发式算法及贪婪方法进行近似求解。