Accuracy of Computed Eigenvectors via Optimizing a Rayleigh Quotient Export

@misc{citeulike:1155316, abstract = {This note gives converses to the well-known result: for any vector e u such that sin `(u; e u) = O(ffl), we have e u Ae u e u e u = + O(ffl 2 ) where is an eigenvalue and u is the corresponding eigenvector of a Hermitian matrix A, and \" \" denotes complex conjugate transpose. It shows that if e u Ae u=e u e u is close to A's largest eigenvalue, then e u is close to the corresponding eigenvector with an error proportional to the square root of the error in e u Ae u=e u ...}, author = {Li, Ren C.}, citeulike-article-id = {1155316}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.2418}, keywords = {quotient, rayleigh}, posted-at = {2007-03-12 12:07:05}, priority = {4}, title = {Accuracy of Computed Eigenvectors via Optimizing a Rayleigh Quotient}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.2418} }

TY - GEN ID - citeulike:1155316 L3 - citeulike-article-id:1155316 N2 - This note gives converses to the well-known result: for any vector e u such that sin `(u; e u) = O(ffl), we have e u Ae u e u e u = + O(ffl 2 ) where is an eigenvalue and u is the corresponding eigenvector of a Hermitian matrix A, and " " denotes complex conjugate transpose. It shows that if e u Ae u=e u e u is close to A's largest eigenvalue, then e u is close to the corresponding eigenvector with an error proportional to the square root of the error in e u Ae u=e u ... TI - Accuracy of Computed Eigenvectors via Optimizing a Rayleigh Quotient KW - quotient KW - rayleigh AU - Li, Ren UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.2418 ER -