Abstract
In this paper, we present a direct method to solve the least-squares Hermitian problem of the complex matrix equation $(AXB,CXD)=(E,F)$ with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, F. This method determines the least-squares Hermitian solution with the minimum norm. It relies on a matrix-vector product and the Moore-Penrose generalized inverse. Numerical experiments are presented which demonstrate the efficiency of the proposed method.
Highlights
Let A, B, C, D, E, and F are given matrices of suitable sizes defined over the complex number field
We are interested in the analysis of the linear matrix equation (AXB, CXD) = (E, F)
From Algorithm ( ), it can be concluded that the complex matrix equation [AXB, CXD] = [E, F] is consistent, and it has a unique solution XH ∈ HE; further, XH – X = . e– can be tested
Summary
Let A, B, C, D, E, and F are given matrices of suitable sizes defined over the complex number field. Problem Given A ∈ Cm×n, B ∈ Cn×s, C ∈ Cm×n, D ∈ Cn×t, E ∈ Cm×s, and F ∈ Cm×t, let HL = X|X ∈ HCn×n, AXB – E + CXD – F = min AX B – E + CX D – F Denote the linear space Cm×n × Cm×t = {[A, B]|A ∈ Cm×n, B ∈ Cm×t}, and for the matrix pairs [Ai, Bi] ∈ Cm×n × Cm×t (i = , ), we can define their inner product as follows: [A , B ], [A , B ] = tr(AH A ) + tr(BH B ).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
