Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

…
Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at

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ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
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doi:10.1553/etna_vol54s128



doi:10.1553/etna_vol54s128


  ETNA 

Thema: natural
Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Sk. Safique Ahmad, Istkhar Ali, Ivan Slapničar
PDF Icon  Perturbation analysis of matrices over a quaternion division algebra ()
S.  128 - 149
doi:10.1553/etna_vol54s128

Open access

Verlag der Österreichischen Akademie der Wissenschaften


doi:10.1553/etna_vol54s128
Abstract:
In this paper, we present the concept of perturbation bounds for the right eigenvalues of a quaternionic matrix. In particular, a Bauer-Fike-type theorem for the right eigenvalues of a diagonalizable quaternionic matrix is derived. In addition, perturbations of a quaternionic matrix are discussed via a block-diagonal decomposition and the Jordan canonical form of a quaternionic matrix. The location of the standard right eigenvalues of a quaternionic matrix and a sufficient condition for the stability of a perturbed quaternionic matrix are given. As an application, perturbation bounds for the zeros of quaternionic polynomials are derived. Finally, we give numerical examples to illustrate our results.

Keywords:  quaternionic matrices, left eigenvalues, right eigenvalues, quaternionic polynomials, Bauer-Fike theorem, quaternionic companion matrices, quaternionic matrix norms
Published Online:  2021/01/21 12:40:08
Object Identifier:  0xc1aa5576 0x003c2af6
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

…


Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at