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Jacobis Algorithm on Compact Lie Algebras

Kleinsteuber, M; Helmke, Uwe; Hueper, Knut

Description

A generalization of the cyclic Jacobi algorithm is proposed that works in an arbitrary compact Lie algebra. This allows, in particular, a unified treatment of Jacobi algorithms on different classes of matrices, e.g., skew-symmetric or skew-Hermitian Hamiltonian matrices. Wildberger has established global, linear convergence of the algorithm for the classical Jacobi method on compact Lie algebras. Here we prove local quadratic convergence for general cyclic Jacobi schemes.

dc.contributor.authorKleinsteuber, M
dc.contributor.authorHelmke, Uwe
dc.contributor.authorHueper, Knut
dc.date.accessioned2015-12-13T22:49:01Z
dc.date.available2015-12-13T22:49:01Z
dc.identifier.issn0895-4798
dc.identifier.urihttp://hdl.handle.net/1885/80344
dc.description.abstractA generalization of the cyclic Jacobi algorithm is proposed that works in an arbitrary compact Lie algebra. This allows, in particular, a unified treatment of Jacobi algorithms on different classes of matrices, e.g., skew-symmetric or skew-Hermitian Hamiltonian matrices. Wildberger has established global, linear convergence of the algorithm for the classical Jacobi method on compact Lie algebras. Here we prove local quadratic convergence for general cyclic Jacobi schemes.
dc.publisherSociety for Industrial and Applied Mathematics
dc.sourceSIAM Journal on Matrix Analysis and Applications
dc.subjectKeywords: Costs; Eigenvalues and eigenfunctions; Hamiltonians; Matrix algebra; Optimization; Parameter estimation; Problem solving; Quadratic programming; Compact Lie algebra; Cost function; Jacobi algorithm; Quadratic convergence; Real root space decomposition; Al Compact Lie algebras; Cost function; Jacobi algorithm; Optimization; Quadratic convergence; Real root space decomposition
dc.titleJacobis Algorithm on Compact Lie Algebras
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume26
dc.date.issued2004
local.identifier.absfor010105 - Group Theory and Generalisations
local.identifier.absfor010301 - Numerical Analysis
local.identifier.ariespublicationMigratedxPub8614
local.type.statusPublished Version
local.contributor.affiliationKleinsteuber, M, University of Wurzburg
local.contributor.affiliationHelmke, Uwe, University of Wurzburg
local.contributor.affiliationHueper, Knut, College of Engineering and Computer Science, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage42
local.bibliographicCitation.lastpage69
local.identifier.doi10.1137/S0895479802420069
dc.date.updated2015-12-11T10:32:17Z
local.identifier.scopusID2-s2.0-14644397962
CollectionsANU Research Publications

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