ELA, Volume 13, pp. 10-39, February 2005, abstract.

Structure Preserving Algorithms for Perplectic Eigenproblems

D. Steven Mackey, Niloufer Mackey, and Daniel M. Dunlavy

Structured real canonical forms for real nxn matrices that 
are symmetric or skew-symmetric about the anti-diagonal 
as well as the main diagonal are presented, and Jacobi 
algorithms for solving the complete eigenproblem for three 
of these four classes of matrices are developed. Based on 
the direct solution of 4x4 subproblems constructed via 
quaternions, the  algorithms calculate structured orthogonal 
bases for the invariant subspaces of the associated matrix.
In addition to preserving structure, these methods are 
inherently parallelizable, numerically stable, and show 
asymptotic quadratic convergence.