Geodesic
A structured staircase algorithm for skew-symmetric/symmetric pencils
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 1-33.

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

Summary: We present structure preserving algorithms for the numerical computation of structured staircase forms of skew-symmetric/symmetric matrix pencils along with the Kronecker indices of the associated skew-symmetric/symmetric Kronecker-like canonical form. These methods allow deflation of the singular structure and deflation of infinite eigenvalues with index greater than one. Two algorithms are proposed: one for general skew-symmetric/symmetric pencils and one for pencils in which the skew-symmetric matrix is a direct sum of and $$########$$§$$###$ \ddot \copyright \copyright $ . We show how to use the structured staircase form to solve boundary value problems arising in control applications and present numerical examples.$$
Classification : 65F15, 15A21, 93B40
Keywords: structured staircase form, linear-quadratic control, control, structured Kronecker canonical form, skew-symmetric/symmetric pencil, skew-Hamiltonian/Hamiltonian pencil 
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     title = {A structured staircase algorithm for skew-symmetric/symmetric pencils},
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Byers, Ralph; Mehrmann, Volker; Xu, Hongguo. A structured staircase algorithm for skew-symmetric/symmetric pencils. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 1-33. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a24/