Geodesic
Structure preserving algorithms for perplectic eigenproblems
The electronic journal of linear algebra, Tome 13 (2005), pp. 10-39.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Structured real canonical forms for matrices in Rn*n that are symmetric or skewsymmetric 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 4 * 4 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.
Classification : 65F15, 15A18, 15A21, 15A57, 15A69
Keywords: canonical form, eigenvalues, eigenvectors, Jacobi method, double structure preserving, symmetric, persymmetric, skew-symmetric, perskew-symmetric, centrosymmetric, perplectic, quaternion, tensor product, Lie algebra, Jordan algebra, bilinear form 
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     title = {Structure preserving algorithms for perplectic eigenproblems},
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Mackey, D.Steven; Mackey, Niloufer; Dunlavy, Daniel M. Structure preserving algorithms for perplectic eigenproblems. The electronic journal of linear algebra, Tome 13 (2005), pp. 10-39. http://geodesic.mathdoc.fr/item/ELA_2005__13__a23/