High‐performance direct algorithms for computing the sign function of triangular matrices

机译：用于计算三角矩阵符号函数的高性能直接算法

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Summary >Algorithms and implementations for computing the sign function of a triangular matrix are fundamental building blocks for computing the sign of arbitrary square real or complex matrices. We present novel recursive and cache‐efficient algorithms that are based on Higham's stabilized specialization of Parlett's substitution algorithm for computing the sign of a triangular matrix. We show that the new recursive algorithms are asymptotically optimal in terms of the number of cache misses that they generate. One algorithm that we present performs more arithmetic than the nonrecursive version, but this allows it to benefit from calling highly optimized matrix multiplication routines; the other performs the same number of operations as the nonrecursive version, suing custom computational kernels instead. We present implementations of both, as well as a cache‐efficient implementation of a block version of Parlett's algorithm. Our experiments demonstrate that the blocked and recursive versions are much faster than the previous algorithms and that the inertia strongly influences their relative performance, as predicted by our analysis. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”XML：ID =“NLA2139-ABS-ABS-0001”> <标题类型=“main”>摘要</ title> >计算符号函数的实现和实现三角矩阵是用于计算任意方形实物或复杂矩阵的标志的基本构建块。我们提出了基于Higham稳定算法的高级稳定算法的新型递归和高效算法，用于计算三角矩阵的符号。我们表明新的递归算法在它们生成的缓存未命中的数量方面是渐近最佳的。我们呈现的一种算法执行比非额外持有者版本更多的算法，但这允许它从调用高度优化的矩阵乘法例程中受益;另一个执行与非持续版本相同数量的操作，适用于自定义计算内核。我们呈现了两者的实现，以及高速缓存的议程算法的高效实现。我们的实验表明，被阻塞和递归版本比以前的算法快得多，并且惯性强烈影响他们的相对性能，如我们分析所预测的那样。</ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-26104/'>《Numerical linear algebra with applications》</a> <b style="margin: 0 2px;">|</b><span>2018年第2期</span><b style="margin: 0 2px;">|</b><span>共17页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Stotland Vadim&option=202" target="_blank" rel="nofollow">Stotland Vadim;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Schwartz Oded&option=202" target="_blank" rel="nofollow">Schwartz Oded;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Toledo Sivan&option=202" target="_blank" rel="nofollow">Toledo Sivan;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Blavatnik School of Computer ScienceTel Aviv UniversityTel Aviv Israel;</p> <p>The Benin School of Computer Science and EngineeringHebrew UniversityJerusalem Israel;</p> <p>Blavatnik School of Computer ScienceTel Aviv UniversityTel Aviv Israel;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/4602.html" title="代数方程论、线性代数">代数方程论、线性代数;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=blocked matrix algorithms&option=203" rel="nofollow">blocked matrix algorithms;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=cache‐efficient algorithms&option=203" rel="nofollow">cache‐efficient algorithms;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=communication‐efficient algorithms&option=203" rel="nofollow">communication‐efficient algorithms;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=matrix functions&option=203" rel="nofollow">matrix functions;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=partitioned matrix algorithms&option=203" rel="nofollow">partitioned matrix algorithms;</a> </p> <div class="translation"> 机译：被阻止的矩阵算法;高速缓存高效算法;通信有效的算法;矩阵函数;分区矩阵算法; </div> </li> </ul> </div> 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