Geodesic
Perturbation of partitioned linear response eigenvalue problems
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 624-638
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.
Classification : 15A42, 65F15
Keywords: linear response eigenvalue problem, random phase approximation, perturbation, quadratic perturbation bound 
@article{ETNA_2015__44__a1,
     author = {Teng,  Zhongming and Lu,  Linzhang and Li,  Ren-Cang},
     title = {Perturbation of partitioned linear response eigenvalue problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {624--638},
     year = {2015},
     volume = {44},
     zbl = {1330.65060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a1/}
}
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Teng,  Zhongming; Lu,  Linzhang; Li,  Ren-Cang. Perturbation of partitioned linear response eigenvalue problems. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 624-638. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a1/