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# EPS_BSE

A structured Bethe-Salpeter eigenvalue problem.

## Notes

The problem is formulated as \(Hx=\lambda x\), where \(H\) has a Bethe-Salpeter structure,

\[\begin{split}H = \begin{bmatrix} R & C \\ -C^* & -R^T \end{bmatrix},\end{split}\]
where \(R\) is Hermitian and \(C\) is complex symmetric. Can also be used in the case of real matrices.

A description of the properties of this problem can be found in [Alvarruiz et al., 2025] and references therein.

## References

[Alv25]

F. Alvarruiz, B. Mellado-Pinto, and J. E. Roman. Variants of thick-restart Lanczos for the Bethe-Salpeter eigenvalue problem. arXiv:2503.20920 : retrieved 27 May 2025, 2025. doi:10.48550/arXiv.2503.20920.

## See Also

EPS: Eigenvalue Problem Solver, Structured Eigenvalue Problems, `EPSProblemType`, `EPSSetProblemType()`

## Level

intermediate

## Location

include/slepceps.h

Index of all EPS routines Table of Contents for all manual pages Index of all manual pages