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.
Author: | Peter Benner, Ralph Byers |
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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 |