标题： 一种简略选择的阿诺尔迪过程 显示英文标题

标题： A sketch-and-select Arnoldi process

摘要： 提出了一种简化的选择Arnoldi过程，以低成本生成Krylov空间的良好条件基。在每次迭代中，该过程利用随机抽样选择有限数量的先前计算的基向量，以从当前基向量中投影出去。计算成本随着Krylov空间的维度线性增长。投影步骤的子集选择问题通过统计学习和压缩感知中使用的多种启发式算法和贪心方法近似解决。 显示英文摘要

摘要： 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.