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

TL;DR

This paper provides a numerical analysis of the parallel orbital-updating method for solving linear eigenvalue problems, demonstrating its convergence and error properties, especially when many eigenpairs are needed.

Contribution

It offers the first detailed convergence and error analysis of the parallel orbital-updating approach for linear eigenvalue problems.

Findings

Proves convergence of the method

Establishes error estimates for numerical approximations

Validates efficiency in eigenvalue computations

Abstract

The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be 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.