Document Zbl 07824620

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Math. Appl.</a> <a href="/?q=in%3A510289" title="Articles in this Issue">159, 44-59 (2024)</a>. </div> <div class="abstract">Summary: In this article, based on the structural properties of the coefficient matrix obtained through the discretization of constrained optimal control problems under the time-harmonic parabolic equation, we propose and compare two types of algorithms, namely the Optimized PU (OPU) method and the optimized double-step (ODS) method. It can be theoretically proven that both of these iterative methods have a convergence rate of 0.1716, which can even be optimized to reach 0.0396. Additionally, we demonstrate that these two methods avoid the common drawback of many methods in terms of parameter selection, where the parameters often depend on the matrix’s eigenvalues. The convergence rate of 0.1716 can be easily achieved through a single constant setup in the proposed two methods. Furthermore, we also compare the algorithmic complexity of the OPU method, the ODS method, and the latest RSS-like method in each step of the iterative process, which demonstrates that the OPU method and ODS method exhibit advantages in computational storage or calculation complexity. Finally, to demonstrate the effectiveness of our proposed optimized iterative methods and the validity of our theoretical findings, we conduct numerical experiments. The results provide strong empirical support for the efficiency and reliability of these methods.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7824620">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65-XX" title="MSC2020">65-XX</a> </td> <td class="space"> Numerical analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92-XX" title="MSC2020">92-XX</a> </td> <td class="space"> Biology and other natural sciences </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aoptimal+control+problem">optimal control problem</a>; <a href="/?q=ut%3Acomplex+linear+equations">complex linear equations</a>; <a href="/?q=ut%3Aiterative+method">iterative method</a>; <a href="/?q=ut%3Aconvergence+analysis">convergence analysis</a></div> <div class="software"> <h3>Software:</h3><a href="/software/9350">MinRes</a>; <a href="/software/4398">IFISS</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 07824620" data-ciurl="/ci/07824620" data-biburl="/bibtex/07824620.bib" data-amsurl="/amsrefs/07824620.bib" data-xmlurl="/xml/07824620.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07824620.pdf" title="Zbl 07824620 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/10.1016/j.camwa.2024.01.017" aria-label="DOI for “Comparisons of two iteration methods for time-harmonic parabolic optimal control problems”" title="10.1016/j.camwa.2024.01.017">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, Numer. 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