Abstract
In this paper, an iterative method is presented to solve the linear matrix equation AXB = C over the generalized reflexive (or anti-reflexive) matrix X (A ? Rpxn, B ? Rmxq, C ? Rpxq, X ? Rnxm). By the iterative method, the solvability of the equation AXB = C over the generalized reflexive (or anti-reflexive) matrix can be determined automatically. When the equation AXB = C is consistent over the generalized reflexive (or anti-reflexive) matrix X, for any generalized reflexive (or anti-reflexive) initial iterative matrix X1, the generalized reflexive (anti-reflexive) solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique least-norm generalized reflexive (or anti-reflexive) iterative solution of AXB = C can be derived when an appropriate initial iterative matrix is chosen. A sufficient and necessary condition for whether the equation AXB = C is inconsistent is given. Furthermore, the optimal approximate solution of AXB = C for a given matrix X0 can be derived by finding the least-norm generalized reflexive (or anti-reflexive) solution of a new corresponding matrix equation AXB = C. Finally, several numerical examples are given to support the theoretical results of this paper.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
