The complex step approximation to the higher order Frechet derivatives of a matrix function
dc.authorid | 0000-0002-7750-4325 | en_US |
dc.contributor.author | Al-Mohy, Awad H. | |
dc.contributor.author | Arslan, Bahar | |
dc.date.accessioned | 2021-03-20T20:09:20Z | |
dc.date.available | 2021-03-20T20:09:20Z | |
dc.date.issued | 2020 | |
dc.department | BTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümü | en_US |
dc.description.abstract | Thekth 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.sponsorship | Deanship of Scientific Research at King Khalid University [R.G.P.1/113/40] | en_US |
dc.description.sponsorship | This work received funding from the Deanship of Scientific Research at King Khalid University through Research Groups Program under Grant No. R.G.P.1/113/40 | en_US |
dc.identifier.doi | 10.1007/s11075-020-00998-3 | en_US |
dc.identifier.issn | 1017-1398 | |
dc.identifier.issn | 1572-9265 | |
dc.identifier.scopusquality | Q2 | en_US |
dc.identifier.uri | http://doi.org/10.1007/s11075-020-00998-3 | |
dc.identifier.uri | https://hdl.handle.net/20.500.12885/376 | |
dc.identifier.wos | WOS:000564517600001 | en_US |
dc.identifier.wosquality | Q1 | en_US |
dc.indekslendigikaynak | Web of Science | en_US |
dc.indekslendigikaynak | Scopus | en_US |
dc.institutionauthor | Arslan, Bahar | |
dc.language.iso | en | en_US |
dc.publisher | Springer | en_US |
dc.relation.ispartof | Numerical Algorithms | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.rights | info:eu-repo/semantics/closedAccess | en_US |
dc.subject | Matrix function | en_US |
dc.subject | Frechet derivative | en_US |
dc.subject | Higher order Frechet derivative | en_US |
dc.subject | Complex step approximation | en_US |
dc.subject | Action of matrix functions | en_US |
dc.title | The complex step approximation to the higher order Frechet derivatives of a matrix function | en_US |
dc.type | Article | en_US |