Estimation, principal components and Hamiltonian systems
type: Item
instance of: scholarly article
title: Estimation, principal components and Hamiltonian systems
zbMATH Open document ID: 0607.93057
DOI: 10.1016/0167-6911(85)90005-2
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: The paper advocates the use of symplectic geometry to analyzing the structure of critical points of the least squares estimation function. The problem dealt with is that of fitting a plane, in particular a line, given a data set in \({\mathbb{C}}^ n\). The basic observation is that for the fitting of a line, the least squares estimation function can be regarded as a Hamiltonian defined on the orbit of the adjoint action of the unitary group.
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 93E10
zbMATH DE Number: 3983047
zbMATH Keywords: complete integrability
zbMATH Keywords: symplectic geometry
zbMATH Keywords: critical points
zbMATH Keywords: least squares estimation
zbMATH Keywords: Hamiltonian
zbMATH Keywords: adjoint action
author: Anthony M. Bloch
reviewed by: Krzysztof Tchoń
MaRDI profile type: Publication
full work available at URL: 0167-6911(85)90005-2
OpenAlex ID: W2044595660
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Wikidata QID: Q125618726
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description: scientific article; zbMATH DE number 3983047