Tight upper bounds for the convergence of the randomized extended Kaczmarz and Gauss–Seidel algorithms

Du Kui

摘要

Summary > The randomized extended Kaczmarz and Gauss–Seidel algorithms have attracted much attention because of their ability to treat all types of linear systems (consistent or inconsistent, full rank or rank deficient). In this paper, we present <fi>tight</fi> upper bounds for the convergence of the randomized extended Kaczmarz and Gauss–Seidel algorithms. Numerical experiments are given to illustrate the theoretical results. </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 =“nla2233-abs-abs-0001”> <标题类型=“main”>摘要</ title> >随机扩展kaczmarz和gauss-seidel 由于能够治疗所有类型的线性系统（一致或不一致，全排名或排名缺陷），算法引起了很多关注。在本文中，我们为随机扩展Kaczmarz和Gauss-Seidel算法的收敛呈现<fi>拧紧</ fi>上限。给出了数值实验来说明理论结果。 </ 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>2019年第3期</span><b style="margin: 0 2px;">|</b><span>共1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=Du Kui&option=202" target="_blank" rel="nofollow">Du Kui;</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>Fujian Provincial Key Laboratory of Mathematical Modeling and High‐Performance Scientific Computing School of Mathematical SciencesXiamen UniversityXiamen China;</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=convergence analysis&option=203" rel="nofollow">convergence analysis;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Moore–Penrose pseudoinverse solution&option=203" rel="nofollow">Moore–Penrose pseudoinverse solution;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=randomized extended Gauss–Seidel algorithm&option=203" rel="nofollow">randomized extended Gauss–Seidel algorithm;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=randomized extended Kaczmarz algorithm&option=203" rel="nofollow">randomized extended Kaczmarz algorithm;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=tight upper bound&option=203" rel="nofollow">tight upper bound;</a> </p> <div class="translation"> 机译：收敛分析;摩尔彭罗斯假灭液;随机扩展高斯 - Seidel算法;随机扩展kaczmarz算法;紧密的上限; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/academic-journal-cn_transactions-nanjing-university-aeronautics-astronautics_thesis/0201280055810.html">一种求解大型离散不适定问题的正则化随机Kaczmarz算法</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘凤鸣&option=202" 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translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：具有侧向接合和上部接合特征的自行车pan可通过侧盖从侧面打开，并通过在上部接合开口上方延伸的上盖在顶部打开;侧盖在关闭状态下横向限制上接合口 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130455489620.html">Method and apparatus for using random access memory for hashing algorithms based on hardware requiring extended functions</a> <b>[P]</b> . <span> 外国专利：  KR970012202A </span> <span> . 1997-03-29</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于需要扩展功能的硬件将随机存取存储器用于哈希算法的方法和装置 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130434049105.html">convergence of weighted random early detection '' puffereinlassung algorithm</a> <b>[P]</b> . <span> 外国专利：  DE60125901D1 </span> <span> . 2007-02-22</span> 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