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arXiv · 1801.00884

Structure-Preserving {\Gamma}QR and {\Gamma}-Lanczos Algorithms for Bethe-Salpeter Eigenvalue Problems

Zhen-Chen Guo·Tiexiang Li·Ying-Ying Zhou
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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 $H=\begin{bmatrix}A & B-\overline{B} & -\overline{A}\end{bmatrix}$, 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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Zhen-Chen Guo, Tiexiang Li, Ying-Ying Zhou. 2018-01-03. Structure-Preserving {\Gamma}QR and {\Gamma}-Lanczos Algorithms for Bethe-Salpeter Eigenvalue Problems. https://arxiv.org/abs/1801.00884

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