A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit <a rel="external noopener" href="https://dipot.ulb.ac.be/dspace/bitstream/2013/200878/3/1502.07405v1.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
<i title="Society for Industrial & Applied Mathematics (SIAM)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wbdvoluxebgjhn3wq3qsnldey4" style="color: black;">SIAM Journal on Scientific Computing</a>
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/15m1010117">doi:10.1137/15m1010117</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wqgn7munmfb7josi3e2ohqg5pi">fatcat:wqgn7munmfb7josi3e2ohqg5pi</a> </span>
more »... ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel R Xeon Phi (MIC). The code is part of a software package called STRUMPACK -STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921234444/https://dipot.ulb.ac.be/dspace/bitstream/2013/200878/3/1502.07405v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8c/fd/8cfde3070ec24dcf889f4d862cc439cc97b75638.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/15m1010117"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>