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dc.contributor.authorMyllykoski, Mirko
dc.contributor.authorRossi, Tuomo
dc.date.accessioned2015-09-03T05:38:00Z
dc.date.available2015-09-03T05:38:00Z
dc.date.issued2014
dc.identifier.citationMyllykoski, M., & Rossi, T. (2014). A parallel radix-4 block cyclic reduction algorithm. <i>Numerical Linear Algebra with Applications</i>, <i>21</i>(4), 540-556. <a href="https://doi.org/10.1002/nla.1909" target="_blank">https://doi.org/10.1002/nla.1909</a>
dc.identifier.otherCONVID_22534584
dc.identifier.otherTUTKAID_57408
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/46747
dc.description.abstractA conventional block cyclic reduction algorithm operates by halving the size of the linear system at each reduction step, that is, the algorithm is a radix-2 method. An algorithm analogous to the block cyclic reduction known as the radix-q partial solution variant of the cyclic reduction (PSCR) method allows the use of higher radix numbers and is thus more suitable for parallel architectures as it requires fever reduction steps. This paper presents an alternative and more intuitive way of deriving a radix-4 block cyclic reduction method for systems with a coefficient matrix of the form tridiag{ − I,D, − I}. This is performed by modifying an existing radix-2 block cyclic reduction method. The resulting algorithm is then parallelized by using the partial fraction technique. The parallel variant is demonstrated to be less computationally expensive when compared to the radix-2 block cyclic reduction method in the sense that the total number of emerging subproblems is reduced. The method is also shown to be numerically stable and equivalent to the radix-4 PSCR method. The numerical results archived correspond to the theoretical expectations.
dc.language.isoeng
dc.publisherJohn Wiley & Sons Ltd.
dc.relation.ispartofseriesNumerical Linear Algebra with Applications
dc.subject.othersyklinen reduktio
dc.subject.othersuora ratkaisija
dc.subject.othernopea Poisson ratkaisija
dc.subject.otherrinnakkaislaskenta
dc.subject.otherosamurtokehitelmätekniikka
dc.subject.otherPSCR
dc.subject.otherblock cyclic reduction
dc.subject.otherdirect solver
dc.subject.otherfast Poisson solver
dc.subject.otherparallel computing
dc.subject.otherpartial fraction technique
dc.titleA parallel radix-4 block cyclic reduction algorithm
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201509022792
dc.contributor.laitosTietotekniikan laitosfi
dc.contributor.laitosDepartment of Mathematical Information Technologyen
dc.contributor.oppiaineTietotekniikkafi
dc.contributor.oppiaineMathematical Information Technologyen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2015-09-02T12:15:04Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange540-556
dc.relation.issn1070-5325
dc.relation.numberinseries4
dc.relation.volume21
dc.type.versionacceptedVersion
dc.rights.copyright© 2013 John Wiley & Sons, Ltd. This is a final draft version of an article whose final and definitive form has been published by Wiley. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1002/nla.1909
dc.type.okmA1


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