## Abstract

A class of quaternion matrices called generalized η -(anti-)bi-Hermitian matrices is defined which incorporates the η -(anti-)bi-Hermitian matrices mentioned by Yuan et al. [Linear Multilinear Algebra. 63;2015:1849–1863] as special cases. In the earlier referred work, Yuan et al. have derived explicit formulas for the least-squares η -(anti-)bi-Hermitian solutions of the coupled matrix equations (AXB, CXD)=(E, F). In this paper, an efficient iterative algorithm is proposed to numerically find the generalized least-squares η -(anti-)bi-Hermitian solutions of the coupled matrix equations (Formula presented.) The validity and efficiency of the presented algorithm is examined by some test experiments.

Original language | English |
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Pages (from-to) | 1743-1769 |

Number of pages | 27 |

Journal | Linear and Multilinear Algebra |

Volume | 65 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2 Sep 2017 |

Externally published | Yes |

## Keywords

- convergence
- generalized -(anti-)bi-Hermitian
- iterative algorithm
- least-squares solution
- Quaternion matrix equations