In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subspace methods have the second order convergence rate which is better than the existing results. These sharper estimates provide a new dependence of convergence rate on the coarse spaces in augmented subspace methods. These new results are also validated by some numerical examples.

翻译：在本文中,为旨在解决电子价值问题的增强子空间方法得出了一些增强的误差估计数。我们将表明,增强的子空间方法具有比现有结果更好的第二顺序趋同率。这些更敏锐的估计数提供了在增强的子空间方法下对粗空空间的新的趋同率的依赖性。这些新的结果也得到了一些数字实例的验证。