Energy Error Estimates of Subspace Method and Multigrid Algorithm for Eigenvalue Problems

Yunhui He, Qichen Hong, Hehu Xie, Meiling Yue, Chunguang You

Published 2017-05-08Version 1

In this paper, we give a new error estimate of the subspace projection method for eigenvalue problem in energy norm. The relationship between the error estimates in $L^2$-norm and energy norm is also derived. Based on these new results, the convergence analysis is provided for the inverse power method on the subspace. Then we present the analysis for the geometric and algebraic multigrid methods for the eigenvalue problem based on the convergence result of the inverse power method on the subspace.