Volume 44, pp. 1-24, 2015.

Structure preserving deflation of infinite eigenvalues in structured pencils

Volker Mehrmann and Hongguo Xu

Abstract

The long standing problem is discussed of how to deflate the part associated with the eigenvalue infinity in a structured matrix pencil using structure preserving unitary transformations. We derive such a deflation procedure and apply this new technique to symmetric, Hermitian or alternating pencils and in a modified form to (anti)-palindromic pencils. We present a detailed error and perturbation analysis of this and other deflation procedures and demonstrate the properties of the new algorithm with several numerical examples.

Full Text (PDF) [375 KB]

Key words

structured staircase form, structured Kronecker canonical form, symmetric pencil, Hermitian pencil, alternating pencil, palindromic pencil, linear quadratic control, $H_\infty$ control

AMS subject classifications

65F15, 15A21, 93B40

Links to the cited ETNA articles

[5]Vol. 26 (2007), pp. 1-33 Ralph Byers, Volker Mehrmann, and Hongguo Xu: A structured staircase algorithm for skew-symmetric/symmetric pencils

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