An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB = E, CXD = F

作者：Chen, Deqin^*; Yin, Feng; Huang, Guang-Xin

来源：Journal of Applied Mathematics, 2012, 492951.

DOI：10.1155/2012/492951

• RECURSIVE BLOCKED ALGORITHMS
• SOLVING TRIANGULAR SYSTEMS
• SYMMETRIC-SOLUTIONS
• MINIMUM-NORM
• SYLVESTER
• A(2)XB(2)
• A(1)XB(1)
• C-1
• PAIR

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 X-1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of AXB = E, CXD = F for a given generalized reflexive matrix X-0 can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair A (X) over tildeB = (E) over tilde, C (X) over tildeD = (F) over tilde with (E) over tilde = E -AX(0)B, (F) over tilde = F -CX0D. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.

• 出版日期2012
• 单位四川轻化工大学; 成都理工大学