<?xml version="1.1" encoding="utf-8"?>
<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">ETI</journal-id><journal-title-group><journal-title>Education and Teaching Innovation</journal-title></journal-title-group><issn>2995-4894</issn><eissn>2995-4908</eissn><publisher><publisher-name>Art and Technology</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.61369/ETI.2025050010</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>一类矩阵方程谱范数下最小二乘解的交替方向算法</title><url>https://artdesignp.com/journal/ETI/3/5/10.61369/ETI.2025050010</url><author>崔学莲</author><pub-date pub-type="publication-year"><year>2025</year></pub-date><volume>3</volume><issue>5</issue><history><date date-type="pub"><published-time>2025-05-20</published-time></date></history><abstract>基于交替方向法给出矩阵方程谱范数下的最小二乘解的表达式，给出计算最小二乘解的数值算法和收敛性证明，并用数值算例加以证明算法的有效性。</abstract><keywords>矩阵方程,谱范数,最小二乘解,交替方向</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>[1]戴华.用振动实验最优校正刚度，柔度和质量矩阵[J].振动工程学报，1998,2:168-768.&amp;nbsp;[2] 朱德懋，孙久厚.动态有限元模型建立的逆方法[J].南京航空学院学报，1986,4:17-24.&amp;nbsp;[3] 蒋正新，陆起超.谱约束下的矩阵最佳逼近问题[J].计算数学，1986,1:168-768.&amp;nbsp;[4] 须田信英.自动控制中的矩阵论理论[M].北京:科学出版社，1979,1-443.&amp;nbsp;[5] CHENEY E W.Introduction to Approximation Theory[J].Chelsea,New York,1996.&amp;nbsp;[6] LIAO A P,BAI Z Z,YUAN L.Best approximate solution of matrix equationAXB+CYD=E[J].SIAM Journal on Matrix Analysis and Application,2005,27: 675-688.&amp;nbsp;[7] 袁世芳,廖安平,雷渊.矩阵方程AXB+CYD=E对称极小范数最小二乘解[J].计算数学，2007,2:203-216.&amp;nbsp;[8] 蒋家尚,袁永新.矩阵方程AXB+CYD=E的对称解(英文)[J].南京大学学报半年刊,2008,2:141-148.&amp;nbsp;[9] PENG Z Y.Solution of symmetry-constrained least-squres problems[J].Numerical Linear Algebra Applications,2008,15:373-389.&amp;nbsp;[10] LI J F,HU X Y,ZHANG L.The submatrix constraint problem of matrix equationAXB+CYD=E [J].Applied Mathematics and Computation,2009,215(7):2578-2590.&amp;nbsp;[11] LI H Y,GAO Z S,ZHAO D.Least squares solutions of the matrix equationAXB+CYD=Ewith the least norm for symmetric arrowhead matrices[J]. Applied Mathematics and&amp;nbsp;Computation,2014,226:719-724.&amp;nbsp;[12] Ke Y F,Ma C F.Alternating direction method for generalized Sylvester matrix equationAXB+CYD=E[J].Applied Mathematics and Computation,2015,260: 565-576.&amp;nbsp;[13] 李姣芬 .两类矩阵逆问题和几类约束矩阵方程问题的理论和新算法[D].长沙：湖南大学,2010,25-39.&amp;nbsp;[14] 高岩 .非光滑优化[M].北京:科学出版社,2008.&amp;nbsp;[15] HAN D,YUAN X,ZHANG W,et al.An ADM-based splitting method for separab- le convex programming[J].Computation Optimization and Applications,2003,54: 343-369.</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
