A sort-Jacobi algorithm for semisimple lie algebras

Abstract

A structure preserving sort-Jacobi algorithm for computing eigenvalues or singular values is presented. It applies to an arbitrary semisimple Lie algebra on its (−1)-eigenspace of the Cartan involution. Local quadratic convergence for arbitrary cyclic schemes is shown for the regular case. The proposed method is independent of the representation of the underlying Lie algebra and generalizes well-known normal form problems such as e.g. the symmetric, Hermitian, skew-symmetric, symmetric and skew-symmetric R -Hamiltonian eigenvalue problem and the singular value decomposition.