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Russian Journal of Numerical Analysis and Mathematical Modelling

Editor-in-Chief: Dymnikov, Valentin P. / Kuznetsov, Yuri

Managing Editor: Vassilevski, Yuri V.

Editorial Board: Agoshkov, Valeri I. / Amosov, Andrey A. / Kaporin, Igor E. / Kobelkov, Georgy M. / Mikhailov, Gennady A. / Repin, Sergey I. / Shaidurov, Vladimir V. / Shokin, Yuri I. / Tyrtyshnikov, Eugene E.

IMPACT FACTOR 2018: 0.779

CiteScore 2018: 0.92

SCImago Journal Rank (SJR) 2018: 0.512
Source Normalized Impact per Paper (SNIP) 2018: 1.275

Mathematical Citation Quotient (MCQ) 2018: 0.08

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Volume 31, Issue 1


Preconditioners for hierarchical matrices based on their extended sparse form

Darya A. Sushnikova / Ivan V. Oseledets
Published Online: 2016-02-16 | DOI: https://doi.org/10.1515/rnam-2016-0003


In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with ℋ2-matrices. We propose several new preconditioners for such matrices that are based on the equivalent sparse extended form of ℋ2-matrices. In the numerical experiments we show that the most efficient approach is based on the so-called reverse-Schur preconditioning technique.

Keywords: ℋ2-matrix; integral equations; preconditioning

MSC 2010: 65R20; 65F08; 78M16


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About the article

Received: 2015-09-28

Accepted: 2015-11-24

Published Online: 2016-02-16

Published in Print: 2016-02-01

Funding: This work was supported by the Russian Science Foundation grant 14-11-00659.

Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 31, Issue 1, Pages 29–40, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: https://doi.org/10.1515/rnam-2016-0003.

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