Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations

e-Archivo Repository

Show simple item record

dc.contributor.author Anguas Márquez, Luis Miguel
dc.contributor.author Bueno Cachadiña, María Isabel
dc.contributor.author Martínez Dopico, Froilán César
dc.date.accessioned 2021-04-05T06:50:45Z
dc.date.available 2021-04-05T06:50:45Z
dc.date.issued 2019-08-26
dc.identifier.bibliographicCitation Anguas, L. M., Bueno, M. I. & Dopico, F. M. (2019). Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations. Mathematics of Computation, 89(322), pp. 767–805.
dc.identifier.issn 0025-5718
dc.identifier.uri http://hdl.handle.net/10016/32248
dc.description.abstract We present the first general study on the effect of Möbius transformations on the eigenvalue condition numbers and backward errors of approximate eigenpairs of polynomial eigenvalue problems (PEPs). By usingthe homogeneous formulation of PEPs, we are able to obtain two clear andsimple results. First, we show that if the matrix inducing the Möbius transformation is well-conditioned, then such transformation approximately preservesthe eigenvalue condition numbers and backward errors when they are definedwith respect to perturbations of the matrix polynomial which are small relativeto the norm of the whole polynomial. However, if the perturbations in eachcoefficient of the matrix polynomial are small relative to the norm of that coefficient, then the corresponding eigenvalue condition numbers and backwarderrors are preserved approximately by the Möbius transformations induced bywell-conditioned matrices only if a penalty factor, depending on the norms ofthose matrix coefficients, is moderate. It is important to note that these simple results are no longer true if a non-homogeneous formulation of the PEP isused.
dc.format.extent 39
dc.language.iso eng
dc.publisher American Mathematical Society
dc.rights © 2019 American Mathematical Society
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Backward error
dc.subject.other Eigenvalue condition number
dc.subject.other Matrix polynomial
dc.subject.other M\"Öbius transformation
dc.subject.other Polynomial eigenvalue problem
dc.title Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1090/mcom/3472
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. MTM2017-90682-REDT
dc.relation.projectID Gobierno de España. BES-2013-065688
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 767
dc.identifier.publicationissue 322
dc.identifier.publicationlastpage 805
dc.identifier.publicationtitle Mathematics of Computation
dc.identifier.publicationvolume 89
dc.identifier.uxxi AR/0000023961
dc.contributor.funder Ministerio de Economía y Competitividad (España)
 Find Full text

Files in this item

*Click on file's image for preview. (Embargoed files's preview is not supported)


The following license files are associated with this item:

This item appears in the following Collection(s)

Show simple item record