Structured Condition Number for a Certain Class of Functions of Non-commuting Matrices

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dc.authorid0000-0002-7750-4325
dc.authorid0000-0001-8132-520X
dc.contributor.authorArslan, Bahar
dc.contributor.authorCardoso, Joao R.
dc.date.accessioned2026-02-12T21:04:52Z
dc.date.available2026-02-12T21:04:52Z
dc.date.issued2023
dc.departmentBursa Teknik Üniversitesi
dc.description.abstractWe investigate the structured condition number of a class of functions of two non-commuting matrices with some type of structure, in order to assess the sensitivity of structured perturbations in the input matrices. This might have interest in several practical applications, like the computation of the geometric mean of two symmetric positive definite matrices or the exp-log mean of two symplectic matrices. These two particular matrix functions deserve a particular study, as well as the matrix-matrix exponentiation. Algorithms for computing the structured condition number are proposed, but they are in general expensive. To round this issue, we derive lower and upper bounds for estimating the structured condition number. Results regarding the comparison between the structured and unstructured condition numbers for pairs of symmetric or skew-symmetric input matrices are provided. Several numerical experiments involving many structured matrices are carried out to compare the structured condition number with the bounds and also with the unstructured condition number.
dc.description.sponsorshipCentre for Mathematics of the University of Coimbra - Portuguese Government through FCT/MCTES
dc.description.sponsorshipThe work of Joao R. Cardoso was partially supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES
dc.identifier.doi10.1007/s00025-023-02020-3
dc.identifier.issn1422-6383
dc.identifier.issn1420-9012
dc.identifier.issue6
dc.identifier.scopus2-s2.0-85173922169
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s00025-023-02020-3
dc.identifier.urihttps://hdl.handle.net/20.500.12885/6699
dc.identifier.volume78
dc.identifier.wosWOS:001082526300001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Basel Ag
dc.relation.ispartofResults in Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260212
dc.subjectFunctions of non-commuting matrices
dc.subjectFrechet derivatives
dc.subjectstructured condition number
dc.subjectgeometric mean
dc.subjectexp-log mean
dc.subjectmatrix-matrix exponentiation
dc.titleStructured Condition Number for a Certain Class of Functions of Non-commuting Matrices
dc.typeArticle

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