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
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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_vol61s66



doi:10.1553/etna_vol61s66



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


Alessandro Buccini, Lothar Reichel
S.  66 - 91
doi:10.1553/etna_vol61s66

Open access

Verlag der Österreichischen Akademie der Wissenschaften


doi:10.1553/etna_vol61s66
Abstract:
This paper describes software for the solution of finite-dimensional minimization problemswith two terms, a fidelity term and a regularization term. The sum of the $p$-norm of theformer and the $q$-norm of the latter is minimized, where $0 < p,q\leq 2$. We note that the“$p$-norm” is not a norm when $ 0< p < 1$, and similarly for the “$q$-norm”. This kind ofminimization problems arises when solving linear discrete ill-posed problems, such ascertain problems in image restoration. They also find applications in statistics.Recently, limited-memory restarted numerical methods that are well suited for the solutionof large-scale minimization problems of this kind were described by the authors in[Adv. Comput. Math., 49 (2023), Art. 26]. Thesemethods are based on the application of restarted generalized Krylov subspaces. This paperpresents software for these solution methods.

Keywords:  $l^p$-$l^q$ minimization, inverse problem, regression, iterative method
  2024/07/03 15:00:46
Object Identifier:  0xc1aa5572 0x003f33ac
.

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