Structure-preserving Gamma QR and Gamma-Lanczos algorithms for Bethe-Salpeter eigenvalue problems

Abstract

To solve the Bethe-Salpeter eigenvalue problem with distinct sizes, two efficient methods, called Gamma QR algorithm and Gamma-Lanczos algorithm, are proposed in this paper. Both algorithms preserve the special structure of the initial matrix. H = [(-(B) over bar) (A) (-(A) over bar) (B)], resulting the computed eigenvalues and the associated eigenvectors still hold the properties similar to those of dr. Theorems are given to demonstrate the validity of the proposed two algorithms in theory. Numerical results are presented to illustrate the superiorities of our methods. (C) 2018 Elsevier B.V. All rights reserved.