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

Bestellung/Order


ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



Send or fax to your local bookseller or to:

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
UID-Nr.: ATU 16251605, FN 71839x Handelsgericht Wien, DVR: 0096385

Bitte senden Sie mir
Please send me
 
Exemplar(e) der genannten Publikation
copy(ies) of the publication overleaf


NAME


ADRESSE / ADDRESS


ORT / CITY


LAND / COUNTRY


ZAHLUNGSMETHODE / METHOD OF PAYMENT
    Visa     Euro / Master     American Express


NUMMER

Ablaufdatum / Expiry date:  

    I will send a cheque           Vorausrechnung / Send me a proforma invoice
 
DATUM, UNTERSCHRIFT / DATE, SIGNATURE

BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
X
BibTEX-Export:

X
EndNote/Zotero-Export:

X
RIS-Export:

X 
Researchgate-Export (COinS)

Permanent QR-Code

doi:10.1553/etna_vol51s451



doi:10.1553/etna_vol51s451



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


Niel Van Buggenhout, Marc Van Barel, Raf Vandebril
PDF Icon  Biorthogonal rational Krylov subspace methods ()
S.  451 - 468
doi:10.1553/etna_vol51s451

Open access

Verlag der Österreichischen Akademie der Wissenschaften


doi:10.1553/etna_vol51s451
Abstract:
A general framework for oblique projections of non-Hermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured pencil, where the structure can take several forms such as Hessenberg or inverse Hessenberg. One specific instance of the structures appearing in this framework for oblique projections is a tridiagonal pencil. This is a direct generalization of the classical biorthogonal Krylov subspace method, where the projection becomes a single non-Hermitian tridiagonal matrix and of the Hessenberg pencil representation for rational Krylov subspaces. Based on the compact storage of this tridiagonal pencil in the biorthogonal setting, we can develop short recurrences. Numerical experiments confirm the validity of the approach.

Keywords:  rational Krylov, biorthogonal, short recurrence, oblique projection, matrix pencil
  2019/12/05 11:34:04
Object Identifier:  0xc1aa5572 0x003b12fe
.

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