Chunguang You

Yunhui He, Qichen Hong, Hehu Xie et al.

This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the stiff matrix, of the subspace projection method for eigenvalue problems is given. The relation between error estimates in $L^2$-norm and energy norm is also deduced. Based on this relation, a new type of inverse power method is designed for eigenvalue problems and the corresponding convergence analysis is also provided. Then we present the analysis of the geometric and algebraic multigrid methods for eigenvalue problems based on the convergence result of the new inverse power method.

Hehu Xie, Chunguang You

This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.