## Perturbation of partitioned linear response eigenvalue problems

Zhongming Teng, Linzhang Lu, and Ren-Cang Li

### Abstract

This paper is concerned with bounds for the linear response eigenvalue problem for $H=\begin{bmatrix} 0 & K \\ M & 0 \end{bmatrix}$, where $K$ and $M$ admit a $2\times 2$ block partitioning. Bounds on how the changes of its eigenvalues are obtained when $K$ and $M$ are perturbed. They are of linear order with respect to the diagonal block perturbations and of quadratic order with respect to the off-diagonal block perturbations in $K$ and $M$. The result is helpful in understanding how the Ritz values move towards eigenvalues in some efficient numerical algorithms for the linear response eigenvalue problem. Numerical experiments are presented to support the analysis.

Full Text (PDF) [420 KB], BibTeX

### Key words

linear response eigenvalue problem, random phase approximation, perturbation, quadratic perturbation bound

15A42, 65F15