Inhalt des Dokuments
Preprint 12-2004
An Arithmetic for Matrix Pencils: Theory and New Algorithms
Author(s) :
Ralph Byers
,
Peter Benner
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 12-2004
MSC 2000
- 65F15 Eigenvalues, eigenvectors
-
65F30 Other matrix algorithms
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.
Keywords :
matrix pencil, matrix sign function, differential algebraic equation