一类矩阵方程自反解的自适应参数交替方向法Adaptive Qarameter Alternating Direction Algorithm for Reflexive Solutions of a Class of Matrix Equations
闫同新;柯艺芬;马昌凤;
摘要(Abstract)：
提出求解一类广义耦合Sylvester矩阵方程自反解的自适应参数交替方向迭代算法,证明算法在适当的条件下是收敛的,并给出了数值实验.
关键词(KeyWords)： Sylvester矩阵方程;自反解;迭代算法;收敛性分析;数值实验
基金项目(Foundation): 国家自然科学基金资助项目(11901098);; 福建省中青年教师教育科研资助项目(JAT190422)
作者(Author): 闫同新;柯艺芬;马昌凤;
Email:
DOI:
参考文献(References)：
- [1]HAJARIAN M.Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations [J].Applied Mathematical Modelling,2015,39 (19):6073-6084.
- [2]KE Y F,MA C F.An alternating direction method for nonnegative solutions of the matrix equation AX + YB = C [J].Computational and Applied Mathematics,2017,36 (1):359-365.
- [3]BAI Z Z.On Hermitian and skew-Hermitian splitting iteration methods for continuous Sylvester equations [J].Journal of Computational Mathematics,2011,29 (2):185-198.
- [4]CHEN B,HARKER P T.Smoothing approximations to nonlinear complementarity problems [J].SIAM Journal on Optimization,1997,7 (1):403-420.
- [5]CHEN X,QI L,SUN D.Global and superlinear convergence of the smoothing Newton method and its application to general box-constrained variational inequalities [J].Mathematics of Computation,1998,67 (1):519-540.
- [6]FERRIS M C,PANG J S.Engineering and economic applications of complementarity problems [J].SIAM Review,1997,39 (3):669-713.
- [7]KANZOW C.Some noninterior continuation methods for linear complementarity problems [J].SIAM Journal on Matrix Analysis and Applications,1994,17 (4):178-193.
- [8]LEON H F O.A delayed weighted gradient method for strictly convex quadratic minimization [J].Computational Optimization and Applications,2019,74(3):729-746.
- [9]LYU L L,ZHANG Z,ZHANG L,et al.An iterative algorithm for periodic sylvester matrix equations [J].Journal of Industrial and Management Optimization,2018,14 (1):413-425.
- [10]XIE Y J,HUANG N,MA C F.Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix [J].Computers and Mathematics with Applications,2014,67 (11):2071-2084.
- [11]ZHOU B,LI Z Y,DUAN G R,et al.Weighted least squares solutions to general coupled Sylvester matrix equations [J].Journal of Computational and Applied Mathematics,2009,224 (2):759-776.
- [12]XU Z,GAO L.The Uzawa-MBB type algorithm for nonsymmetric saddle point problems [J].Computational Optimization and Applications,2019,73 (3):933-956.