Jacobi's algorithm on compact lie algebras

M. Kleinsteuber; U. Helmke; K. Hüper

doi:10.1137/S0895479802420069

Jacobi's algorithm on compact lie algebras

M. Kleinsteuber^*, U. Helmke, K. Hüper

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	42-69
Number of pages	28
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	26
Issue number	1
DOIs	https://doi.org/10.1137/S0895479802420069
Publication status	Published - 2005
Externally published	Yes

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title = "Jacobi's algorithm on compact lie algebras",

abstract = "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.",

keywords = "Compact Lie algebras, Cost function, Jacobi algorithm, Optimization, Quadratic convergence, Real root space decomposition",

author = "M. Kleinsteuber and U. Helmke and K. H{\"u}per",

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AU - Kleinsteuber, M.

AU - Helmke, U.

AU - Hüper, K.

PY - 2005

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N2 - 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.

AB - 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.

KW - Compact Lie algebras

KW - Cost function

KW - Jacobi algorithm

KW - Optimization

KW - Quadratic convergence

KW - Real root space decomposition

UR - https://www.scopus.com/pages/publications/14644397962

U2 - 10.1137/S0895479802420069

DO - 10.1137/S0895479802420069

M3 - Article

SN - 0895-4798

VL - 26

SP - 42

EP - 69

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 1

ER -

Jacobi's algorithm on compact lie algebras

Abstract

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