Structure-preserving ΓQR and Γ-Lanczos algorithms for Bethe-Salpeter eigenvalue problems

Abstract To solve the Bethe–Salpeter eigenvalue problem with distinct sizes, two efficient methods, called Γ QR algorithm and Γ -Lanczos algorithm, are proposed in this paper. Both algorithms preserve the special structure of the initial matrix ℋ = A B − B ¯ − A ¯ , resulting the computed eigenvalues and the associated eigenvectors still hold the properties similar to those of ℋ . 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.

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