Jacobis Algorithm on Compact Lie Algebras
Date
2004
Authors
Kleinsteuber, M
Helmke, Uwe
Hueper, Knut
Journal Title
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Volume Title
Publisher
Society for Industrial and Applied Mathematics
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.
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Keywords
Keywords: 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
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Source
SIAM Journal on Matrix Analysis and Applications
Type
Journal article
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DOI
10.1137/S0895479802420069