Volume 44, pp. 624-638, 2015.

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 $H=\left[\begin{array}{cc}0& K\\ M& 0\end{array}\right]$, 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.

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Key words

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

AMS subject classifications

15A42, 65F15

ETNA articles which cite this article

Vol. 46 (2017), pp. 505-523 Zhongming Teng and Lei-Hong Zhang: A block Lanczos method for the linear response eigenvalue problem