Article(id=1242117238073918048, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242117211490419171, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1242576000000, receivedDateStr=2009-05-18, revisedDate=1253548800000, revisedDateStr=2009-09-22, acceptedDate=null, acceptedDateStr=null, onlineDate=1254067200000, onlineDateStr=2009-09-28, pubDate=1254067200000, pubDateStr=2009-09-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1254067200000, onlineIssueDateStr=2009-09-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774073426977, creator=sys-migrate, updateTime=1774073426977, updator=sys-migrate, issue=Issue{id=1242117211490419171, tenantId=1146029695717560320, journalId=1146031591421210625, year='2009', volume='27', issue='0918', pageStart='3', pageEnd='140', issueExtLink='null', onlineDate='null', pubDate='1254067200000', pubDateStr='2009-09-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774073420636, creator='sys-migrate', updateTime=1774073420636, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=90, endPage=93, ext={EN=ArticleExt(id=1242117243371327509, articleId=1242117238073918048, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=A Parallel Chasing Algorithm for Solving Cyclic Tridiagonal Equations, columnId=1242116080374710456, journalTitle=Science & Technology Review, columnName=Articles, runingTitle=null, highlight=null, articleAbstract=A parallel algorithm for solving the cyclic tridiagonal equations is developed in this paper. This algorithm is mainly based on the matrix decomposition. Firstly, a lower order cyclic tridiagonal equation can be formed by extracting the first and the last equation in each process. Secondly, the lower order cyclic tridiagonal equation is solved to obtain the values of the key variables. Finally, the values of the key variables are used in the corresponding processes and the related equations are solved in parallel. The cyclic tridiagonal equations can be solved efficiently and stably by using this algorithm if the coefficient matrix is diagonally dominant, which condition is also required by the traditional chasing method, so, the parallel algorithm developed in this paper to solve the tridiagonal equations does not need additional conditions to restrict the coefficient matrix. The computational cost of the parallel algorithm in one process is only O(17n) and equal to that of the traditional algorithm for solving the cyclic tridiagonal equations. Moreover, the distributed parallel computation can also be performed and the data communication cost is small. In fact, the data length for the communication from child processes to the master process and from the master process to child processes is 8 real numbers and 2 real numbers, respectively. Therefore, the computational cost and the data communication cost are smaller than the traditional parallel algorithm for solving the cyclic tridiagonal equations. The numerical experiments indicate that，as far as large scale cyclical tridiagonal equations are considered, the parallel computational efficiency is greater than 0.75 if the rank number is less than 16. Indeed, the traditional chasing algorithm is a particular case of this algorithm. So, this algorithm can be used to solve the tridiagonal equations naturally., authors=null, authorsList=null, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=N9h3jfxANzfSRtaUU8xGeA==, pdfFileSize=340408, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242117241005740036, articleId=1242117238073918048, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=追赶法并行求解循环三对角方程组, columnId=1146540929516700224, journalTitle=科技导报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=给出了求解循环三对角线性方程组的一种并行算法。在系数矩阵满足对角占优的条件下，利用该方法能够快速、稳定地求解循环三对角线性方程组，在单个进程上的计算量仅为O(17n)，与传统算法求解循环三对角线性方程组的计算量相同。而且，本算法可以方便地实施分布式并行计算，各进程仅需向主进程传递8个实数，而主进程向各子进程传递2个实数，通讯量较小。数值实验结果表明：对于大规模的循环三对角线性方程组，利用16个进程计算的并行效率均在0.75以上。求解三对角线性方程组的传统追赶法实则是本文算法的一种特例，因此，该算法也可用于求解三对角线性方程组。, authors=李文强,刘晓, authorsList=李文强;刘晓, authorCompany=河南师范大学数学与与信息科学学院, correspAuthors=null, authorNote=null, correspAuthorsNote=李文强, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=KFKUvyOQ6N71McLLNzdC9g==, pdfFileSize=340408, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null)}, authors=null, keywords=[Keyword(id=1242117240745694208, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242117238073918048, language=CN, orderNo=1, 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