An efficient iterative algorithm for quaternionic least-squares problems over the generalized -(anti-)bi-Hermitian matrices

Salman Ahmadi-Asl, Fatemeh Panjeh Ali Beik

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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 languageEnglish
Pages (from-to)1743-1769
Number of pages27
JournalLinear and Multilinear Algebra
Volume65
Issue number9
DOIs
Publication statusPublished - 2 Sep 2017
Externally publishedYes

Keywords

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

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