TY - JOUR
T1 - Jacobi's algorithm on compact lie algebras
AU - Kleinsteuber, M.
AU - Helmke, U.
AU - Hüper, K.
PY - 2005
Y1 - 2005
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 - http://www.scopus.com/inward/record.url?scp=14644397962&partnerID=8YFLogxK
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 -