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Main Title: Solving singular generalized eigenvalue problems by a rank-completing perturbation
Author(s): Hochstenbach, Michiel
Mehl, Christian
Plestenjak, Bor
Type: Research Paper
Abstract: Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may sometimes be time-demanding, even for small and medium-sized matrices. We propose a simple method to compute the eigenvalues of singular pencils, based on one perturbation of the original problem of a certain specific rank. For many problems, the method is both fast and robust. This approach may be seen as a welcome alternative to staircase methods.
Subject(s): singular pencil
singular generalized eigenvalue problem
rank-completing perturbation
model updating
double eigenvalues
two-parameter eigenvalue problem
differential algebraic equations
quadratic two-parameter eigenvalue problem
Issue Date: 22-May-2018
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A18 Eigenvalues, singular values, and eigenvectors
65F15 Eigenvalues, eigenvectors
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2018, 03
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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