A matrix LSQR iterative method to solve matrix equation AXB = C

作者：Peng, Zhen-Yun^*

来源：International Journal of Computer Mathematics, 2010, 87(8): 1820-1830.

DOI：10.1080/00207160802516875

• iterative method
• LSQR algorithm
• matrix equation
• least-squares problem
• matrix nearness problem

This paper is a matrix iterative method presented to compute the solutions of the matrix equation, AXB = C, with unknown matrix X is an element of S, where S is the constrained matrices set like symmetric, symmetric-R-symmetric and (R, S)-symmetric. By this iterative method, for any initial matrix X(0) is an element of S, a solution X* can be obtained within finite iteration steps if exact arithmetics were used, and the solution X* with the minimum Frobenius norm can be obtained by choosing a special kind of initial matrix. The solution (X) over cap, which is nearest to a given matrix (X) over tilde in Frobenius norm, can be obtained by first finding the minimum Frobenius norm solution of a new compatible matrix equation. The numerical examples given here show that the iterative method proposed in this paper has faster convergence and higher accuracy than the iterative methods proposed in [G.-X. Huang, F. Yin, and K. Guo, An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation AXB = C, J. Comput. Appl. Math. 212 (2008), pp. 231-244; Y. Lei and A.-P. Liao, A minimal residual algorithm for the inconsistent matrix equation AXB = C over symmetric matrices, Appl. Math. Comput. 188 (2007), pp. 499-513; Z.-Y. Peng, An iterative method for the least squares symmetric solution of the linear matrix equation AXB = C, Appl. Math. Comput. 170 (2005), pp. 711-723; Y.-X. Peng, X.-Y. Hu, and L. Zhang, An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C, Appl. Math. Comput. 160 (2005), pp. 763-777].

• 出版日期2010
• 单位桂林电子科技大学