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https://hdl.handle.net/1959.11/5457
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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Machado, Luís | en |
dc.contributor.author | Silva Leite, Fátima | en |
dc.contributor.author | Krakowski, Krzysztof | en |
dc.date.accessioned | 2010-04-06T16:36:00Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Journal of Dynamical and Control Systems, 16(1), p. 121-148 | en |
dc.identifier.issn | 1573-8698 | en |
dc.identifier.issn | 1079-2724 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/5457 | - |
dc.description.abstract | In this paper, we present a generalization of the classical least squares problem on Euclidean spaces, introduced by Lagrange, to more general Riemannian manifolds. Using the variational definition of Riemannian polynomials, we formulate a higher-order variational problem on a manifold equipped with a Riemannian metric, which depends on a smoothing parameter and gives rise to what we call smoothing geometric splines. These are curves with a certain degree of smoothness that best fit a given set of points at given instants of time and reduce to Riemannian polynomials when restricted to each subinterval. We show that the Riemannian mean of the given points is achieved as a limiting process of the above. Also, when the Riemannian manifold is an Euclidean space, our approach generates, in the limit, the unique polynomial curve which is the solution of the classical least squares problem. These results support our belief that the approach presented in this paper is the natural generalization of the classical least squares problem to Riemannian manifolds. | en |
dc.language | en | en |
dc.publisher | Springer | en |
dc.relation.ispartof | Journal of Dynamical and Control Systems | en |
dc.title | Higher-order smoothing splines versus least squares problems on Riemannian manifolds | en |
dc.type | Journal Article | en |
dc.identifier.doi | 10.1007/s10883-010-9080-1 | en |
dc.subject.keywords | Calculus of Variations, Systems Theory and Control Theory | en |
dc.subject.keywords | Algebraic and Differential Geometry | en |
local.contributor.firstname | Luís | en |
local.contributor.firstname | Fátima | en |
local.contributor.firstname | Krzysztof | en |
local.subject.for2008 | 010203 Calculus of Variations, Systems Theory and Control Theory | en |
local.subject.for2008 | 010102 Algebraic and Differential Geometry | en |
local.subject.seo2008 | 970101 Expanding Knowledge in the Mathematical Sciences | en |
local.profile.school | Computer Science | en |
local.profile.email | lmiguel@utad.pt | en |
local.profile.email | fleite@nmail.mat.uc.pt | en |
local.profile.email | kkrakows@une.edu.au | en |
local.output.category | C1 | en |
local.record.place | au | en |
local.record.institution | University of New England | en |
local.identifier.epublicationsrecord | une-20100406-103222 | en |
local.publisher.place | United States of America | en |
local.format.startpage | 121 | en |
local.format.endpage | 148 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 16 | en |
local.identifier.issue | 1 | en |
local.contributor.lastname | Machado | en |
local.contributor.lastname | Silva Leite | en |
local.contributor.lastname | Krakowski | en |
dc.identifier.staff | une-id:kkrakows | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.identifier.unepublicationid | une:5587 | en |
dc.identifier.academiclevel | Academic | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Higher-order smoothing splines versus least squares problems on Riemannian manifolds | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.search.author | Machado, Luís | en |
local.search.author | Silva Leite, Fátima | en |
local.search.author | Krakowski, Krzysztof | en |
local.uneassociation | Unknown | en |
local.identifier.wosid | 000273787700007 | en |
local.year.published | 2010 | en |
Appears in Collections: | Journal Article |
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