# New iterative algorithms for coupled matrix equations

## Related Articles

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This paper is concerned with the numerical solution of the Sylvester tensor equation, which includes the Sylvester matrix equation as special case. By applying hierarchical identification principle proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm...

- On the Hermitian positive defnite solution of the nonlinear matrix equation X + A* X-1 A + B* X-1 B = I. Jian-hui Long; Xi-yan Hu; Lei Zhang // Bulletin of the Brazilian Mathematical Society;Sep2008, Vol. 39 Issue 3, p371
In this paper, we study the matrix equation X + A* X-1 A + B* X-1 B = I, where A, B are square matrices, and obtain some conditions for the existence of the positive definite solution of this equation. Two iterative algorithms to find the positive definite solution are given. Some numerical...

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This paper is concerned with numerical solutions to the generalized coupled Sylvester matrix equations{âˆ‘i=1m(A1,iXB1,i+C1,iYD1,i)=E1âˆ‘i=1m(A2,iXB2,i+C2,iYD2,i)=E2and the periodic coupled matrix...

- A modified iterative algorithm for the (Hermitian) reflexive solution of the generalized Sylvester matrix equation. Beik, Fatemeh Panjeh Ali // Transactions of the Institute of Measurement & Control;Aug2014, Vol. 36 Issue 6, p815
Recently, Ramadan et al. have focused on the following matrix equation:A1V+A2VÂ¯+B1W+B2WÂ¯=E1VF1+E2VÂ¯F2+Cand propounded two gradient-based iterative algorithms for solving the above matrix equation over reflexive and Hermitian reflexive matrices, respectively. In this paper, we develop...

- An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F. Deqin Chen; Feng Yin; Huang, Guang-Xin // Journal of Applied Mathematics;2012, p1
An iterative algorithm is constructed to solve the linear matrix equation pair AXB=E, CXD=F over generalized reflexive matrix X. When the matrix equation pair AXB=E, CXD=F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the...

- Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices. Ning Li; Qing-Wen Wang // Abstract & Applied Analysis;2013, p1
The matrix equation ..., which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation ... over generalized (P,Q)-reflexivematrices. The...

- A finite iterative algorithm for solving the least-norm generalized (P, Q) reflexive solution of the matrix equations AiXBi = Ci. Yong-gong Peng; Xiang Wang // Journal of Computational Analysis & Applications;Nov2014, Vol. 17 Issue 3, p547
In this paper, based on the idea of conjugate gradient method, an algorithm for solving the least-norm generalized (P, Q) reflexive solution of the matrix equations AiXBi = Ci (i = 1, ..., N). According to the algorithm, the solvability of the problem can be determined automatically, i.e., the...

- A NEW METHOD FOR SOLVING MATRIX EQUATION AXB + CXT D = E. Minghui Wang // Mathematical & Computational Applications;Apr2013, Vol. 18 Issue 1, p12
In this paper, we propose a new iterative algorithm to solve the matrix equation AXB + CXT D = E. The algorithm can obtain the minimal Frobenius norm solution or the least-squares solution with minimal Frobenius norm. Our algorithm is better than Algorithm II of the paper [M. Wang, etc.,...

- An Iterative Method for the Least-Squares Problems of a General Matrix Equation Subjects to Submatrix Constraints. Li-fang Dai; Mao-lin Liang; Yong-hong Shen // Journal of Applied Mathematics;2013, p1
An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation Î£ti-1MiZiNi = F, where Zi(i = 1,2,...,t ) are to be determined centro-symmetric matrices with given central principal submatrices. For any initial iterative matrices, we show that the...