Jacobi's Algorithm on Compact Lie Algebras

@article{Kleinsteuber2004JacobisAO,
  title={Jacobi's Algorithm on Compact Lie Algebras},
  author={Martin Kleinsteuber and Uwe Helmke and Knut H{\"u}per},
  journal={SIAM J. Matrix Analysis Applications},
  year={2004},
  volume={26},
  pages={42-69}
}
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, such as, 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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SHOWING 1-10 OF 35 REFERENCES

Lie Groups

  • J. J. Duistermaat, J.A.C. Kolk
  • Springer, Berlin,
  • 2000
Highly Influential
6 Excerpts

A Calculus Approach to Matrix Eigenvalue Algorithms

  • K. Hüper
  • Habilitation thesis, Dep. of Mathematics, W…
  • 2002
2 Excerpts

A Jacobi-type method for computing balanced realizations

  • U. Helmke, K. Hüper
  • Systems & Control Letters, 39:19–30,
  • 2000
1 Excerpt

The Jacobi Method: A Tool for Computation and Control

  • U. Helmke, K. Hüper
  • In: Systems and Control in the Twenty-First…
  • 1997
1 Excerpt

Lie Groups Beyond an Introduction

  • A. W. Knapp
  • Birkhäuser, Boston,
  • 1996
2 Excerpts

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