Bunch–Nielsen–Sorensen formula: Difference between revisions
Content deleted Content added
created page with minimal description and references |
(No difference)
|
Revision as of 23:38, 18 November 2013
In mathematics, in particular linear algebra, the Bunch-Nielsen-Sorensen formula,[1] named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen expresses the eigenvectors of the sum of a symmetric matrix and the outer product, , of vector with itself.
Statement
Let denote the eigenvalues of and denote the eigenvalues of the updated matrix . In the special case when is diagonal, the eigenvectors of can be written
where is a number that makes the vector normamlized.
Derivation
This formula can be derived from the Sherman–Morrison formula by examining the poles of .
Remarks
The eigenvalues of were studied by Golub[2].
Numerical stability of the computation is studied by Gu and Eisenstadt[3].
See also
References
- ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/BF01396012 , please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/BF01396012
instead. - ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1137/1015032, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1137/1015032
instead. - ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1137/S089547989223924X, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1137/S089547989223924X
instead.