Peng, Zhenyun; Hu, Xiyan; Zhang, Lei The nearest bisymmetric solutions of linear matrix equations. (English) Zbl 1068.65057 J. Comput. Math. 22, No. 6, 873-880 (2004). Necessary and sufficient conditions for the existence of bisymmetric solutions as well as expressions for such solutions are derived for the equations (1) \(A_1X_1B_1+\cdots +A_kX_kB+k= D\), (2) \(A_1\times B_1+\cdots+ A_k\times B_k= D\) and (3) \((A_1\times B_1,\dots, A_k\times B_k)= (D_1,\dots, D_k)\). They are based on Kronecker products and Moore-Penrose generalized inverses. The closest solution of these equations to a given matrix in the Frobenius norm is also provided. Numerical examples illustrate the methodology. Reviewer: Ferenc Szidarovszky (Tucson) Cited in 3 Documents MSC: 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities Keywords:bisymmetric matrices; matrix equations; bisymmetric solutions; Kronecker products; Moore-Penrose generalized inverses; closest solution; Frobenius norm; numerical examples PDFBibTeX XMLCite \textit{Z. Peng} et al., J. Comput. Math. 22, No. 6, 873--880 (2004; Zbl 1068.65057)