Enhanced Error Estimates for Augmented Subspace Method

TL;DR

This paper improves the theoretical understanding of augmented subspace methods for eigenvalue problems by deriving sharper error estimates that demonstrate second-order convergence, validated through numerical examples.

Contribution

It introduces enhanced error estimates showing second-order convergence for augmented subspace methods, improving upon previous results.

Findings

Augmented subspace methods have second-order convergence.

Sharper error estimates depend on coarse space properties.

Numerical examples validate the improved estimates.

Abstract

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.