GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method

TL;DR

GCGE is a parallel eigensolver package designed for efficiently computing many eigenpairs of large symmetric matrices, combining damping, subspace projection, and inverse power methods with dynamic shifts.

Contribution

The paper introduces GCGE, a novel eigensolver package that integrates damping, subspace projection, and dynamic shifts to improve large-scale eigenvalue computations.

Findings

Demonstrates high efficiency and stability in large-scale eigenpair computations.

Shows scalability for large symmetric matrices in practical applications.

Provides numerical evidence of superior performance over existing methods.

Abstract

We propose an eigensolver and the corresponding package, GCGE, for solving large scale eigenvalue problems. This method is the combination of damping idea, subspace projection method and inverse power method with dynamic shifts. To reduce the dimensions of projection subspaces, a moving mechanism is developed when the number of desired eigenpairs is large. The numerical methods, implementing techniques and the structure of the package are presented. Plenty of numerical results are provided to demonstrate the efficiency, stability and scalability of the concerned eigensolver and the package GCGE for computing many eigenpairs of large symmetric matrices arising from applications.