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A Bi-Orthogonal Structure-Preserving eigensolver for large-scale linear response eigenvalue problem
Yu Li, Zijing Wang, Yong Zhang
https://arxiv.org/abs/2506.08355

A Bi-Orthogonal Structure-Preserving eigensolver for large-scale linear response eigenvalue problem
The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging numerically for large-scale sparse/dense system, especially when it has zero eigenvalues. Based on a direct sum decomposition of biorthogonal invariant subspaces and the minimization principles in the biorthogonal complement, using the structure of generalized nullspace, we propose a Bi-Orthogonal Structure-Preserving subspace iterative solver, which is stable, efficient, and o…

An efficient Fourier spectral algorithm for the Bogoliubov-de Gennes excitation eigenvalue problem
Yu Li, Zhixuan Li, Manting Xie, Yong Zhang
https://arxiv.org/abs/2506.08308

An efficient Fourier spectral algorithm for the Bogoliubov-de Gennes excitation eigenvalue problem
In this paper, we propose an efficient Fourier spectral algorithm for an eigenvalue problem, that is, the Bogoliubov-de Gennes (BdG) equation arsing from spin-1 Bose-Einstein condensates (BEC) to describe the elementary/collective excitations around the mean-field ground state. The BdG equation is essentially a constrained eigenvalue/eigenfunction system. Firstly, we investigate its analytical properties, including exact eigenpairs, generalized nullspace, and bi-orthogonality of eigenspaces. Se…