File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1137/110841370
- Scopus: eid_2-s2.0-84865466823
- WOS: WOS:000305996500003
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Perturbation analysis for antitriangular Schur decomposition
Title | Perturbation analysis for antitriangular Schur decomposition |
---|---|
Authors | |
Keywords | Antitriangular Schur form Condition number Perturbation analysis |
Issue Date | 2012 |
Citation | SIAM Journal on Matrix Analysis and Applications, 2012, v. 33, n. 2, p. 325-335 How to Cite? |
Abstract | Let Z be an n × n complex matrix. A decomposition Z = ŪMU H is called an antitriangular Schur decomposition of Z if U is an n × n unitary matrix and M is an n × n antitriangular matrix. The antitriangular Schur decomposition is a useful tool for solving palindromic eigenvalue problems. However, there is no perturbation result for an antitriangular Schur decomposition in the literature. The main contribution of this paper is to give a perturbation bound of such decomposition and show that the bound depends inversely on f(M) := min ∥XN∥ F=1 ∥(Aup(MX L - X̄ UM), Aup(M TX L - X̄ UM T))∥ F, where X L and X U are the strictly lower triangular and upper triangular parts of X, X N = X L + X U, and Aup(Y ) denotes the strictly upper antitriangular part of Y. The quantity √2/f(M) can be used to characterize the condition number of the decomposition, i.e., when √2/f(M) is large (or small), the decomposition problem is ill-conditioned (or well-conditioned). Numerical examples are presented to illustrate the theoretical result. © 2012 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276930 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.042 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chen, Xiao Shan | - |
dc.contributor.author | Li, Wen | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:35:05Z | - |
dc.date.available | 2019-09-18T08:35:05Z | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | SIAM Journal on Matrix Analysis and Applications, 2012, v. 33, n. 2, p. 325-335 | - |
dc.identifier.issn | 0895-4798 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276930 | - |
dc.description.abstract | Let Z be an n × n complex matrix. A decomposition Z = ŪMU H is called an antitriangular Schur decomposition of Z if U is an n × n unitary matrix and M is an n × n antitriangular matrix. The antitriangular Schur decomposition is a useful tool for solving palindromic eigenvalue problems. However, there is no perturbation result for an antitriangular Schur decomposition in the literature. The main contribution of this paper is to give a perturbation bound of such decomposition and show that the bound depends inversely on f(M) := min ∥XN∥ F=1 ∥(Aup(MX L - X̄ UM), Aup(M TX L - X̄ UM T))∥ F, where X L and X U are the strictly lower triangular and upper triangular parts of X, X N = X L + X U, and Aup(Y ) denotes the strictly upper antitriangular part of Y. The quantity √2/f(M) can be used to characterize the condition number of the decomposition, i.e., when √2/f(M) is large (or small), the decomposition problem is ill-conditioned (or well-conditioned). Numerical examples are presented to illustrate the theoretical result. © 2012 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Matrix Analysis and Applications | - |
dc.subject | Antitriangular Schur form | - |
dc.subject | Condition number | - |
dc.subject | Perturbation analysis | - |
dc.title | Perturbation analysis for antitriangular Schur decomposition | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/110841370 | - |
dc.identifier.scopus | eid_2-s2.0-84865466823 | - |
dc.identifier.volume | 33 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 325 | - |
dc.identifier.epage | 335 | - |
dc.identifier.eissn | 1095-7162 | - |
dc.identifier.isi | WOS:000305996500003 | - |
dc.identifier.issnl | 0895-4798 | - |