Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32451
Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

Authors: Minghui Wang, Luping Xu, Juntao Zhang


Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 692


[1] Y.F. Xu, An inverse eigenvalue problem for a special kind of matrices. Math. Appl., 1(1996)68-75.
[2] C.J. Meng, X.Y. Hu, L. Zhang, The skew symmetric orthogonal solution of the matrix equation AXB=C, Linear Algebra Appl. 402(2005)303-318.
[3] Li Jiaofen, Zhang Xiaoning, Peng Zhenyun, Alternative projection algorithm for single variable linear constraints matrix equation problems, Mathematica Numerical Since, 36(2014)143-162.
[4] Y.X. Peng, X.Y. Hu, L. Zhang, An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=C, Applied Mathematics and Computation, 160(2005)763-777.
[5] Z.Y. Peng, A matrix LSQR iterative method to solve matrix equation AXB=C, International Journal of Computer Mathematics, 87(2010)1820-1830.
[6] J.F. Li, X.F. Duan, L. Zhang, Numerical solutions of AXB=C for mirror symmetric matrix under a specified submatrix constraint. Computing, 90(2010) 39-56.
[7] Von Neumann J., Functional Operators. II. The Geometry of Spaces, Annals of Mathematics Studies, vol.22, Princeton University Press, Princeton, 1950.
[8] Cheney W., Goldstein A. Proximity maps for convex sets, Proceedings of the American Mathematical Society, 10(1959)448-450.
[9] Hongyi Li, Zongsheng Gao, Di Zhao, Least squares solutions of the matrix equation with the least norm for symmetric arrowhead matrices. Appl. Math. Comput., 226(2014)719-724.