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An Arithmetic for Matrix Pencils: Theory and New Algorithms

Please always quote using this URN:urn:nbn:de:0296-matheon-1323
  • This paper introduces arithmetic-like operations on matrix pencils. The pencil-arithmetic operations extend elementary formulas for sums and products of rational numbers and include the algebra of linear transformations as a special case. These operation give an unusual perspective on a variety of pencil related computations. We derive generalizations of monodromy matrices and the matrix exponential. A new algorithm for computing a pencilarithmetic generalization of the matrix sign function does not use matrix inverses and gives an empirically forward numerically stable algorithm for extracting deflating subspaces.

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Metadaten
Author:Peter Benner, Ralph Byers
URN:urn:nbn:de:0296-matheon-1323
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/04/29
Release Date:2004/04/27
Preprint Number:122
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