Numerical Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems

The parallel orbital-updating approach is an orbital iteration based approach for solving eigenvalue problems when many eigenpairs are required, and has been proven to be very efficient, for instance, in electronic structure calculations. In this paper, based on the investigation of a quasi-orthogonality, we present the numerical analysis of the parallel orbital-updating approach for linear eigenvalue problems, including convergence and error estimates of the numerical approximations.