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Main Title: An Arithmetic for Matrix Pencils: Theory and New Algorithms
Author(s): Byers, Ralph
Benner, Peter
Type: Research Paper
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.
Subject(s): matrix pencil
matrix sign function
differential algebraic equation
Issue Date: 26-Apr-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F15 Eigenvalues, eigenvectors
65F30 Other matrix algorithms
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 12
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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