TY - JOUR
A2 - Yuan, Jinyun
AU - Chen, Deqin
AU - Yin, Feng
AU - Huang, Guang-Xin
PY - 2012
DA - 2012/07/15
TI - An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations ,
SP - 492951
VL - 2012
AB - 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 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 X0 can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair AX̃B=Ẽ, CX̃D=F̃ with Ẽ=E-AX0B, F̃=F-CX0D. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.
SN - 1110-757X
UR - https://doi.org/10.1155/2012/492951
DO - 10.1155/2012/492951
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -