Article(id=1242120614178263055, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242120596776096697, 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=1271001600000, receivedDateStr=2010-04-12, revisedDate=1280592000000, revisedDateStr=2010-08-01, acceptedDate=null, acceptedDateStr=null, onlineDate=1285603200000, onlineDateStr=2010-09-28, pubDate=1285603200000, pubDateStr=2010-09-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1285603200000, onlineIssueDateStr=2010-09-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774074231901, creator=sys-migrate, updateTime=1774074231901, updator=sys-migrate, issue=Issue{id=1242120596776096697, tenantId=1146029695717560320, journalId=1146031591421210625, year='2010', volume='28', issue='18', pageStart='3', pageEnd='140', issueExtLink='null', onlineDate='null', pubDate='1285603200000', pubDateStr='2010-09-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774074227753, creator='sys-migrate', updateTime=1774074227753, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=60, endPage=63, ext={EN=ArticleExt(id=1242120616594182175, articleId=1242120614178263055, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=Forward Elimination and Backward Substitution Algorithm for Solving the Quasi-pentadiagonal Linear Equations, columnId=1242116080374710456, journalTitle=Science & Technology Review, columnName=Articles, runingTitle=null, highlight=null, articleAbstract= Based on the features of quasi-pentadiagonal matrix and the idea of forward elimination and backward substitution algorithm, an algorithm for solving the quasi-pentadiagonal linear equations is proposed in this paper. This algorithm consists of the following two steps. First, the quasi-pentadiagonal matrix A, as the coefficient matrix of the linear equations, is decomposed into three simple matrices
L, U, D with A=LUD, where L is the lower triangular matrix, U is the upper triangular matrix, D is the unit quasi-diagonal matrix. Then, the quasi-pentadiagonal linear equations are decomposed into the following three simpler linear equations: Lz=f, Uy=z, Dx=y. Two equations are solved in the traditional LU decomposition algorithm, while three linear equations are solved in this algorithm, but without increasing the complexity. The total computational cost is only O(39n), less than that of the traditional algorithm. The main idea of this
algorithm is the same as that of the forward elimination and backward substitution algorithm, consequently, the algorithm proposed in this paper is stable if the coefficient matrix is a strictly diagonally dominant matrix. The stability analysis and the corresponding results are also presented in this paper. Numerical experiments indicate that a linear relation is preserved between the computational time and the order n of equations., 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=UHTu4OHs8zJbwJYKa66baQ==, pdfFileSize=365314, 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=1242120615914704921, articleId=1242120614178263055, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=追赶法求解拟五对角线性方程组, columnId=1146540929516700224, journalTitle=科技导报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=根据拟五对角矩阵的特点，沿用追赶法的思想，首先将拟五对角系数矩阵分解成3个简单矩阵的乘积A=LUD，其中L为下三角形矩阵，U为单位上三角形矩阵，D为拟对角矩阵。然后将拟五对角线性方程组的求解问题转化为求解以下3个简单的线性方程组：Lz=f，Uy=z，Dx=y。通常的LU分解仅求解2个方程，本算法虽然将问题转化为3个方程组的求解，复杂度却没有增加，总的运算量仅为O（39n）。由于算法沿用追赶法矩阵分解的思想，对于严格对角占优的五对角线性方程组具有良好的数值稳定性。数值结果表明，算法的计算时间与方程组阶数n呈线性关系。, authors=^{李文强1，马 民1，李卫霞2}, authorsList=李文强;马 民;李卫霞, authorCompany=1. 河南师范大学数学与信息科学学院，河南新乡 4530072. 河南师范大学附属中学，河南新乡 453007, correspAuthors=null, authorNote=null, correspAuthorsNote=李文强, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=+vtO2zGiurOqRhdwKSCSPQ==, pdfFileSize=365314, 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=1242120615541411860, tenantId=1146029695717560320, journalId=1146031591421210625, 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