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**An efficient algorithm for the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\).**
*(English)*
Zbl 1268.65060

Summary: We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\). When the matrix equation is consistent over the reflexive matrix \(X\), a reflexive solution can be obtained within finite iteration steps in the absence of roundoff errors. By the proposed iterative algorithm, the least Frobenius norm reflexive solution of the matrix equation can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate reflexive solution to a given reflexive matrix \(X_0\) can be derived by finding the least Frobenius norm reflexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.

### MSC:

65F30 | Other matrix algorithms (MSC2010) |

15A24 | Matrix equations and identities |

15B33 | Matrices over special rings (quaternions, finite fields, etc.) |

### Keywords:

iterative algorithm; reflexive solution; quaternion matrix equation; least Frobenius norm solution; numerical examples
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\textit{N. Li} et al., J. Appl. Math. 2013, Article ID 217540, 14 p. (2013; Zbl 1268.65060)

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### References:

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