• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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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.

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Verlag der Österreichischen Akademie der Wissenschaften
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ETNA - Electronic Transactions on Numerical Analysis



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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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Pseudo-linear convergence of an additive Schwarz method for dual total variation minimization

    Jongho Park

ETNA - Electronic Transactions on Numerical Analysis, pp. 176-197, 2021/02/03

doi: 10.1553/etna_vol54s176

doi: 10.1553/etna_vol54s176


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doi:10.1553/etna_vol54s176



doi:10.1553/etna_vol54s176

Abstract

In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation. The O(1/n)-energy convergence of the proposed method is proven, where n is the number of iterations. In addition, we introduce an interesting convergence property of the proposed method called pseudo-linear convergence; the energy decreases as fast as for linearly convergent algorithms until it reaches a particular value. It is shown that this particular value depends on the overlapping width δ, and the proposed method becomes as efficient as linearly convergent algorithms if δ is large. As the latest domain decomposition methods for total variation minimization are sublinearly convergent, the proposed method outperforms them in the sense of the energy decay. Numerical experiments which support our theoretical results are provided.

Keywords: domain decomposition method, additive Schwarz method, total variation minimization, Rudin–Osher–Fatemi model, convergence rate

Published Online: 2021/02/03 08:56:21

Object Identifier: 0xc1aa5572 0x003c32d6

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