中文摘要：

本文用R^m×n表示全体m×n实矩阵的集合,Q^m×n表示全体m×n四元数矩阵的集合,R2^n×n表示全体n阶三对角实矩阵的集合,Q3^n×n表示全体n阶三对角四元数矩阵的集合,

英文摘要：

By applying a new way of vec（ABC） presented by Yuan et al.[Yuan,S.F., Liao,A.P.,Lei,Y.Least squares Hermitian solution of the matrix equation（AXB,CXD）= （E,F） with the least norm over the skew field of quaternions.Mathematical and Computer Modelling,2008,48：91-100],Moore-Penrose generalized inverse and Kronecker product of matrices,this paper derives the expressions of the least squares tridiagonal Hermitian solution and least squares tridiagonal bi-Hermitian solution of quaternion matrix equation AXB = C with the least norm,respectively.