A generalized conjugate gradient method for eigenvalue problems

Abstract

A generalized conjugate gradient method is proposed to solve eigenvalue problems. This method is designed bycombining the dumping block inverse power scheme and the subspace projection method. Furthermore, based on theproperties of the proposed method, a series of optimization techniques are developed toimprove the stability, computing efficiency and scalability. We also introducea computing package GCGE (generalized conjugate gradient eigensolver)which is developed based on the proposed method here.Some numerical examples are provided to validate the stability, computing efficiency and scalabilityof the method in this paper. The corresponding computing package can be downloaded from the website <uri xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=http://https://github.com/pase2017/GCGE-1.0>https://github.com/pase2017/GCGE-1.0</uri>