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@techreport { 11303_15541,
author = {Byers, Ralph AND Benner, Peter},
title = {An Arithmetic for Matrix Pencils: Theory and New Algorithms},
institution = {Technische UniversitÃ¤t Berlin},
year = {2004},
doi = {10.14279/depositonce-14314},
url = {http://dx.doi.org/10.14279/depositonce-14314},
keywords = {matrix pencil, matrix sign function, differential algebraic equation, algorithm, arithmetics},
abstract = {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 operations 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 pencil arithmetic generalization of the matrix sign function does not use matrix inverses and gives an empirically forward numerically stable algorithm for extracting deflating subspaces.}
}