Document Zbl 1229.65102

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J. Adapt. Control Signal Process.</a> <a href="/?q=in%3A284802" title="Articles in this Issue">25, No. 8, 707-722 (2011)</a>. </div> <div class="abstract">Summary: We propose a fast and efficient algorithm named the adaptive parallel Krylov-metric projection algorithm. The proposed algorithm is derived from the variable-metric adaptive projected subgradient method, which has recently been presented as a unified analytic tool for various adaptive filtering algorithms. The proposed algorithm features parallel projection – in a variable-metric sense – onto multiple closed convex sets containing the optimal filter with high probability. The metric is designed based on (i) sparsification by means of a certain data-dependent Krylov subspace and (ii) maximal use of the obtained sparse structure for fast convergence. The numerical examples show the advantages of the proposed algorithm over the existing ones in stationary/nonstationary environments.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65K05" title="MSC2020">65K05</a> </td> <td class="space"> Numerical mathematical programming methods </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C25" title="MSC2020">90C25</a> </td> <td class="space"> Convex programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Avariable-metric+projection">variable-metric projection</a>; <a href="/?q=ut%3Aset-theoretic+adaptive+filtering">set-theoretic adaptive filtering</a>; <a href="/?q=ut%3Asubgradient+projection">subgradient projection</a>; <a href="/?q=ut%3Aalgorithm">algorithm</a>; <a href="/?q=ut%3Aadaptive+filtering+algorithms">adaptive filtering algorithms</a>; <a href="/?q=ut%3AKrylov+subspace">Krylov subspace</a>; <a href="/?q=ut%3Anumerical+examples">numerical examples</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 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title="10.1002/acs.1237">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">Haykin, Adaptive Filter Theory (2002) · <a href="/0723.93070" class="nowrap">Zbl 0723.93070</a></td> </tr><tr> <td>[2]</td> <td class="space">Sayed, Adaptive Filters (2008) · <a href="https://doi.org/10.1002/9780470374122" class="nowrap">doi:10.1002/9780470374122</a></td> </tr><tr> <td>[3]</td> <td class="space">Yamada, An efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques, IEEE Transactions on Signal Processing 50 (5) pp 1091– (2002) · <a href="https://doi.org/10.1109/78.995065" class="nowrap">doi:10.1109/78.995065</a></td> </tr><tr> <td>[4]</td> <td class="space">Yukawa, Pairwise optimal weight realization-acceleration technique for set-theoretic adaptive parallel subgradient projection algorithm, IEEE Transactions on Signal Processing 54 (12) pp 4557– 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Document Zbl 1229.65102 - zbMATH Open