The complex step approximation to the higher order Frechet derivatives of a matrix function

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dc.authorid0000-0002-7750-4325en_US
dc.contributor.authorAl-Mohy, Awad H.
dc.contributor.authorArslan, Bahar
dc.date.accessioned2021-03-20T20:09:20Z
dc.date.available2021-03-20T20:09:20Z
dc.date.issued2021
dc.departmentBTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractThekth Frechet derivative of a matrix functionfis a multilinear operator from a cartesian product ofksubsets of the spaceDOUBLE-STRUCK CAPITAL C-nxn into itself. We show that thekth Frechet derivative of a real-valued matrix functionfat a real matrixAin real direction matrices E-1, E-2, horizontal ellipsis, E-k can be computed using the complex step approximation. We exploit the algorithm of Higham and Relton (SIAM J. Matrix Anal. Appl.35(3):1019-1037,2014) with the complex step approximation and mixed derivative of complex step and central finite difference scheme. Comparing with their approach, our cost analysis and numerical experiment reveal thathalfandseven-eighthsof the computational cost can be saved for the complex step and mixed derivative, respectively. Whenfhas an algorithm that computes its action on a vector, the computational cost drops down significantly as the dimension of the problem andkincrease.en_US
dc.description.sponsorshipDeanship of Scientific Research at King Khalid University [R.G.P.1/113/40]en_US
dc.description.sponsorshipThis work received funding from the Deanship of Scientific Research at King Khalid University through Research Groups Program under Grant No. R.G.P.1/113/40en_US
dc.identifier.doi10.1007/s11075-020-00998-3en_US
dc.identifier.endpage1074
dc.identifier.issn1017-1398
dc.identifier.issn1572-9265
dc.identifier.issue3
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1061
dc.identifier.urihttp://doi.org/10.1007/s11075-020-00998-3
dc.identifier.urihttps://hdl.handle.net/20.500.12885/376
dc.identifier.volume87
dc.identifier.wosWOS:000564517600001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorArslan, Bahar
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofNumerical Algorithmsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectMatrix functionen_US
dc.subjectFrechet derivativeen_US
dc.subjectHigher order Frechet derivativeen_US
dc.subjectComplex step approximationen_US
dc.subjectAction of matrix functionsen_US
dc.titleThe complex step approximation to the higher order Frechet derivatives of a matrix functionen_US
dc.typeArticleen_US

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