Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/95876
DC FieldValueLanguage
dc.contributor.authorCardoso, João R.-
dc.contributor.authorMiraldo, Pedro-
dc.date.accessioned2021-10-11T15:52:59Z-
dc.date.available2021-10-11T15:52:59Z-
dc.date.issued2022-
dc.identifier.issn03770427pt
dc.identifier.urihttp://hdl.handle.net/10316/95876-
dc.description.abstractWe propose three iterative methods for solving the Moser-Veselov equation, which arises in the discretization of the Euler-Arnold differential equations governing the motion of a generalized rigid body. We start by formulating the problem as an optimization problem with orthogonal constraints and proving that the objective function is convex. Then, using techniques from optimization on Riemannian manifolds, the three feasible algorithms are designed. The first one splits the orthogonal constraints using the Bregman method, whereas the other two methods are of the steepest-descent type. The second method uses the Cayley-transform to preserve the constraints and a Barzilai-Borwein step size, while the third one involves geodesics, with the step size computed by Armijo’s rule. Finally, a set of numerical experiments are carried out to compare the performance of the proposed algorithms, suggesting that the first algorithm has the best performance in terms of accuracy and number of iterations. An essential advantage of these iterative methods is that they work even when the conditions for applicability of the direct methods available in the literature are not satisfied.pt
dc.language.isoengpt
dc.publisherElsevierpt
dc.relationCMUC-UIDB/00324/2020pt
dc.rightsopenAccesspt
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt
dc.subjectDiscrete Euler-Arnold equationspt
dc.subjectMatrix equationpt
dc.subjectMoser-Veselov equationpt
dc.subjectOptimization with orthogonal constraintpt
dc.subjectOrthogonal matricespt
dc.subjectSkew-symmetric matricespt
dc.titleSolving the discrete Euler–Arnold equations for the generalized rigid body motionpt
dc.typearticle-
degois.publication.firstPage113814pt
degois.publication.titleJournal of Computational and Applied Mathematicspt
dc.peerreviewedyespt
dc.identifier.doi10.1016/j.cam.2021.113814pt
degois.publication.volume402pt
dc.date.embargo2022-01-01*
uc.date.periodoEmbargo0pt
item.languageiso639-1en-
item.fulltextCom Texto completo-
item.grantfulltextopen-
crisitem.author.researchunitCMUC - Centre for Mathematics of the University of Coimbra-
crisitem.author.orcid0000-0001-8132-520X-
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais
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This item is licensed under a Creative Commons License Creative Commons