arXiv subjects

Fernando Alvarruiz

Publications and source records attributed to Fernando Alvarruiz.

4 recordsLinked to original sources

arXiv2026

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

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.

math.NA↗

arXiv2025

Solvers for the Hermitian and the pseudo-Hermitian Bethe-Salpeter equation in the Yambo code: Implementation and Performance

We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. We consider both the Hermitian (Tamm-Dancoff approximation) and pseudo-Hermitian forms, addressing dense matrices of three different sizes. A description of the implementation is also provided, with details for the pseudo-Hermitian case. Timing and memory utilization are analyzed on both CPU and GPU clusters. Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5.

cond-mat.mtrl-sci↗

arXiv2025

Variants of thick-restart Lanczos for the Bethe-Salpeter eigenvalue problem

The non-Hermitian Bethe-Salpeter eigenvalue problem, in the definite case, is a structured eigenproblem, with real eigenvalues coming in pairs $\{\lambda,-\lambda\}$ where the corresponding pair of eigenvectors are closely related, and furthermore the left eigenvectors can be trivially obtained from the right ones. We exploit these properties to devise three variants of structure-preserving Lanczos eigensolvers to compute a subset of eigenvalues (those of either smallest or largest magnitude) together with their corresponding right and left eigenvectors. For this to be effective in real applications, we need to incorporate a thick-restart technique in a way that the overall computation preserves the problem structure. The new methods are validated in an implementation within the SLEPc library using several test matrices, some of them coming from the Yambo materials science code.

math.NA↗

arXiv2023

Thick-restarted joint Lanczos bidiagonalization for the GSVD

The computation of the partial generalized singular value decomposition (GSVD) of large-scale matrix pairs can be approached by means of iterative methods based on expanding subspaces, particularly Krylov subspaces. We consider the joint Lanczos bidiagonalization method, and analyze the feasibility of adapting the thick restart technique that is being used successfully in the context of other linear algebra problems. Numerical experiments illustrate the effectiveness of the proposed method. We also compare the new method with an alternative solution via equivalent eigenvalue problems, considering accuracy as well as computational performance. The analysis is done using a parallel implementation in the SLEPc library.

math.NA↗