ETNA - Electronic Transactions on Numerical Analysis
|
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 |
|
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)
|
ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Stefan Kindermann,
Werner Zellinger
S. 327 - 350 doi:10.1553/etna_vol60s327 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol60s327
Abstract: Motivated by the aggregation method, we present an iterative method for finding approximate solutions of least-squares problems for linear ill-posed problems over (mixed) rational Krylov spaces. The mixed rational Krylov spaces where the solution is sought consist of Tikhonov-regularized solutions mixed with usual Krylov space elements from the normal equations. We present an algorithm based on the Arnoldi–Lanczos iteration, and, as main result, derive the rational CG method, a short-term iteration that, similar as the usual conjugate gradient method, does not requires orthogonalization or saving of the Krylov basis vectors. Some numerical experiments illustrate the performance of the method. Keywords: rational Krylov space, rational conjugate gradient method, aggregation method, short-term recurrence Published Online: 2024/06/06 11:58:56 Object Identifier: 0xc1aa5572 0x003f2511 Rights: . 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 |