Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures
| dc.contributor.author | Bora, Shreemayee | |
| dc.contributor.author | Karow, Michael | |
| dc.contributor.author | Mehl, Christian | |
| dc.contributor.author | Sharma, Punit | |
| dc.date.accessioned | 2017-12-14T15:54:31Z | |
| dc.date.available | 2017-12-14T15:54:31Z | |
| dc.date.issued | 2014-04-17 | |
| dc.description.abstract | We derive a formula for the backward error of a complex number λ when considered as an approximate eigenvalue of a Hermitian matrix pencil or polynomial with respect to Hermitian perturbations. The same are also obtained for approximate eigenvalues of matrix pencils and polynomials with related structures like skew-Hermitian, *-even, and *-odd. Numerical experiments suggest that in many cases there is a significant difference between the backward errors with respect to perturbations that preserve structure and those with respect to arbitrary perturbations. | en |
| dc.identifier.eissn | 1095-7162 | |
| dc.identifier.issn | 0895-4798 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/7279 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-6552 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 512 Algebra | de |
| dc.subject.ddc | 518 Numerische Analysis | de |
| dc.subject.other | Hermitian matrix pencil | en |
| dc.subject.other | perturbation theory | en |
| dc.subject.other | eigenvalue backward error | en |
| dc.subject.other | structured mapping problem | en |
| dc.subject.other | Hermitian matrix polynomial | en |
| dc.title | Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1137/130925621 | en |
| dcterms.bibliographicCitation.issue | 2 | en |
| dcterms.bibliographicCitation.journaltitle | SIAM Journal on Matrix Analysis and Applications | en |
| dcterms.bibliographicCitation.originalpublishername | Society for Industrial and Applied Mathematics | en |
| dcterms.bibliographicCitation.originalpublisherplace | Philadelphia, Pa. | en |
| dcterms.bibliographicCitation.pageend | 475 | en |
| dcterms.bibliographicCitation.pagestart | 453 | en |
| dcterms.bibliographicCitation.volume | 35 | en |
| tub.accessrights.dnb | domain | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Lineare Algebra | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Numerische Lineare Algebra | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |