Enhanced Error Estimates for Augmented Subspace Method

In this paper, some enhanced error estimates are derived for the augmented subspace methods which designed solving eigenvalue problems. For first time, we strictly prove that have second order convergence rate between two iteration steps, is better than existing theoretical results in Lin and Xie (Math Comp 84:71–88, 2015), et al. (SIAM J Numer Anal 57(6):2519–2550, 2019), Xu Sci Comput 42(5):A2655–A2677, 2020) more consistent with of actual numerical test. These sharper explicitly depict dependence on coarse spaces, provides new advantages methods. Some examples finally presented to validate these estimate efficiency our algorithms.