Volume 3,Issue 5
Fall 2025
一类矩阵方程谱范数下最小二乘解的交替方向算法
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。
[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.
[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.
[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.
[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.
[5] CHENEY E W.Introduction to Approximation Theory[J].Chelsea,New York,1996.
[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.
[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.
[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.
[9] PENG Z Y.Solution of symmetry-constrained least-squres problems[J].Numerical Linear Algebra Applications,2008,15:373-389.
[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.
[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
Computation,2014,226:719-724.
[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.
[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.
[14] 高岩 .非光滑优化[M].北京:科学出版社,2008.
[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.