摘要
In this paper,we introduce some strategies to improve the efficiency and scalability of the generalized conjugate gradient algorithm and build a package GCGE for solving large scale eigenvalue problems.This method is the combination of damping idea,subspace projection method and inverse power algorithm 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.
基金
supported partly by National Key R&D Program of China 2019YFA0709600,2019YFA0709601,Science Challenge Project(No.TZ2016002)
the National Center for Mathematics and Interdisciplinary Science,CAS,and Tianjin Education Commission Scientific Research Plan(2017KJ236).
