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Author(s):
Kleinsteuber, Martin 
Title:
A sort-Jacobi algorithm for semisimple Lie algebras. 
Abstract:
The classical Jacobi algorithm is extended to an unified Lie algebraic approach. The conventional Jacobi algorithm minimize the distance to diagonality; they reduce the off-norm, i. e. the sum of squares of off-diagonal entries. Sorting the diagonal elements after each step would accelerate the convergence but, there are difficulties to apply this sorting to the off-norm, that has to minimize. Using the gradient flow of a trace function [it R. W. Brockett, ``Dynamical systems that sort lists, d...    »
 
Keywords:
sort-Jacobi algorithm; Cartan decomposition; restricted-root space; off-norm; trace function; structured eigenvalue decomposition; structured singular value decomposition; local quadratic convergence; exceptional Lie algebra 
Journal title:
Linear Algebra Appl. 
Year:
2009 
Journal volume:
430 
Journal issue:
Pages contribution:
155-173 
Language:
English