Volume 14, Number 4, 2024, Pages  DOI：10.11948/JAAC20230106 
A new BCR method for coupled operator equations with submatrix constraint 
Wenling Wang,Caiqin Song,Wenli Wang 
Keywords:Operator matrix equations, BCR algorithm, Leastnorm constraint solutions, Submatrix constraint 
Abstract: 
In the present work, a new biconjugate residual algorithm (BCR) is proposed in order to compute the constraint solution of the coupled operator equations, in which the constraint solution include symmetric solution, reflective solution, centrosymmetric solution and anticentrosymmetric solution as special cases. When the studied coupled operator equations are consistent, it is proved that constraint solution can be convergent to the exact solutions if giving any initial complex matrices or real matrices. In addition, when the studied coupled operator equations are not consistent, the least norm constraint solution above can also be computed by selecting any initial matrices. Finally, some numerical examples are provided for illustrating the effectiveness and superiority of new proposed method. 
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