Document Zbl 1476.65066

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Appl. Math. Comput.</a> <a href="/?q=in%3A472567" title="Articles in this Issue">3, No. 1, 137-156 (2021)</a>. </div> <div class="abstract">Summary: The generalized singular value decomposition (GSVD) of two matrices with the same number of columns is a very useful tool in many practical applications. However, the GSVD may suffer from heavy computational time and memory requirement when the scale of the matrices is quite large. In this paper, we use random projections to capture the most of the action of the matrices and propose randomized algorithms for computing a low-rank approximation of the GSVD. Serval error bounds of the approximation are also presented for the proposed randomized algorithms. Finally, some experimental results show that the proposed randomized algorithms can achieve a good accuracy with less computational cost and storage requirement.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7432633">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F55" title="MSC2020">65F55</a> </td> <td class="space"> Numerical methods for low-rank matrix approximation; matrix compression </td> </tr><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%3A65F22" title="MSC2020">65F22</a> </td> <td class="space"> Ill-posedness and regularization problems in numerical linear algebra </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F50" title="MSC2020">65F50</a> </td> <td class="space"> Computational methods for sparse matrices </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneralized+singular+value+decomposition">generalized singular value decomposition</a>; <a href="/?q=ut%3Arandomized+algorithm">randomized algorithm</a>; <a href="/?q=ut%3Alow-rank+approximation">low-rank approximation</a>; <a href="/?q=ut%3Aerror+analysis">error analysis</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 1476.65066" data-ciurl="/ci/07432633" data-biburl="/bibtex/07432633.bib" data-amsurl="/amsrefs/07432633.bib" data-xmlurl="/xml/07432633.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07432633.pdf" title="Zbl 1476.65066 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/s42967-020-00061-x" aria-label="DOI for “Randomized generalized singular value decomposition”" title="10.1007/s42967-020-00061-x">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">Bai, ZJ; Demmel, JW, Computing the generalized singular value decomposition, SIAM J. 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