Document Zbl 1410.65103

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Algorithms</a> <a href="/?q=in%3A431266" title="Articles in this Issue">80, No. 4, 1143-1154 (2019)</a>. </div> <div class="abstract">Summary: In this note, the additive block diagonal preconditioner [<span class="zbmathjax-textit">Z.-Z. Bai</span> et al., Numer. Algorithms 62, No. 4, 655–675 (2013; <a href="/1267.65034">Zbl 1267.65034</a>)] and the block triangular preconditioner [<span class="zbmathjax-textit">J. W. Pearson</span> and <span class="zbmathjax-textit">A. J. Wathen</span>, Numer. Linear Algebra Appl. 19, No. 5, 816–829 (2012; <a href="/1274.65187">Zbl 1274.65187</a>)] are further studied and optimized, respectively. The eigenvalue properties of these two preconditioned matrices are analyzed by new way and an expression of the quasi-optimal parameter is derived. Particularly, when $W - T$ or $T - W$ is symmetric positive semidefinite, the exact eigenvalue bounds are obtained which are tighter than the state of the art. At last, numerical experiments are presented to show the effectiveness of the two proposed optimized preconditioners.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7042043">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F10" title="MSC2020">65F10</a> </td> <td class="space"> Iterative numerical methods for linear systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F08" title="MSC2020">65F08</a> </td> <td class="space"> Preconditioners for iterative methods </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apreconditioner">preconditioner</a>; <a href="/?q=ut%3Acomplex+symmetric+problem">complex symmetric problem</a>; <a href="/?q=ut%3Aoptimal+parameter">optimal parameter</a>; <a href="/?q=ut%3Acondition+number">condition number</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1267.65034">Zbl 1267.65034</a>; <a href="/1274.65187">Zbl 1274.65187</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1410.65103" data-ciurl="/ci/07042043" data-biburl="/bibtex/07042043.bib" data-amsurl="/amsrefs/07042043.bib" data-xmlurl="/xml/07042043.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07042043.pdf" title="Zbl 1410.65103 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s11075-018-0520-4" aria-label="DOI for “A note on block diagonal and block triangular preconditioners for complex symmetric linear systems”" title="10.1007/s11075-018-0520-4">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Axelsson, O., Kucherov, A.: Real valued iterative methods for solving complex symmetric linear systems. 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