%0 Journal Article %1 ipsen09 %A Ipsen, I. C. F. %A Nadler, B. %D 2009 %I Society for Industrial and Applied Mathematics %J SIAM Journal on Matrix Analysis and Applications %K eigenvalues perturbation %N 1 %P 40-53 %R 10.1137/070682745 %T Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices %V 31 %X We present eigenvalue bounds for perturbations of Hermitian matrices and express the change in eigenvalues in terms of a projection of the perturbation onto a particular eigenspace, rather than in terms of the full perturbation. The perturbations we consider are Hermitian of rank one, and Hermitian or non-Hermitian with norm smaller than the spectral gap of a specific eigenvalue. Applications include principal component analysis under a spiked covariance model, and pseudo-arclength continuation methods for the solution of nonlinear systems.

@article{ipsen09, abstract = {We present eigenvalue bounds for perturbations of Hermitian matrices and express the change in eigenvalues in terms of a projection of the perturbation onto a particular eigenspace, rather than in terms of the full perturbation. The perturbations we consider are Hermitian of rank one, and Hermitian or non-Hermitian with norm smaller than the spectral gap of a specific eigenvalue. Applications include principal component analysis under a spiked covariance model, and pseudo-arclength continuation methods for the solution of nonlinear systems.}, added-at = {2014-01-26T20:10:04.000+0100}, author = {Ipsen, I. C. F. and Nadler, B.}, biburl = {https://www.bibsonomy.org/bibtex/2f9fd53aec06b47deca45d4e5a26df8e4/ytyoun}, doi = {10.1137/070682745}, interhash = {00a6aeaca3d80a32781b730a449f78eb}, intrahash = {f9fd53aec06b47deca45d4e5a26df8e4}, journal = {SIAM Journal on Matrix Analysis and Applications}, keywords = {eigenvalues perturbation}, month = jan, number = 1, pages = {40-53}, publisher = {Society for Industrial and Applied Mathematics}, timestamp = {2015-07-19T10:14:45.000+0200}, title = {Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices}, volume = 31, year = 2009 }