A structure-preserving Chebyshev-filtered subspace iteration for the Bethe-Salpeter eigenvalue problem

Blanca Mellado-Pinto; Fernando Alvarruiz; Jose E. Roman

A structure-preserving Chebyshev-filtered subspace iteration for the Bethe-Salpeter eigenvalue problem

Numerical Analysis 2026-06-27 v1

Authors: Blanca Mellado-Pinto , Fernando Alvarruiz , Jose E. Roman

Abstract

The Bethe-Salpeter equation, which has many applications in both theoretical and applied physics, is generally solved via a matrix eigenvalue problem with a rich algebraic structure. The numerical solution of such structured eigenproblem calls for specific algorithms that are able to preserve the structure throughout the computation. Several structure-preserving methods have already been proposed in the literature. In this paper, we develop a polynomial filter strategy that is able to extract approximations of eigenvalues located inside a specified interval. For this, we have devised a structure-preserving Chebyshev polynomial series, along with a specialized subspace iteration method that preserves the Bethe-Salpeter structure at every step of the algorithm. All necessary details required for a robust implementation are incorporated, and the performance is illustrated with matrices arising from real applications.

Cite

@article{arxiv.2606.29025,
  title  = {A structure-preserving Chebyshev-filtered subspace iteration for the Bethe-Salpeter eigenvalue problem},
  author = {Blanca Mellado-Pinto and Fernando Alvarruiz and Jose E. Roman},
  journal= {arXiv preprint arXiv:2606.29025},
  year   = {2026}
}