TITLE:
Efficient Solutions of Coupled Matrix and Matrix Differential Equations
AUTHORS:
Zeyad Al-Zhour
KEYWORDS:
Matrix Products; Least-Squares Problem; Coupled Matrix and Matrix Differential Equations; Diagonal Extraction Operator
JOURNAL NAME:
Intelligent Control and Automation,
Vol.3 No.2,
May
23,
2012
ABSTRACT: In Kronecker products works, matrices are sometimes regarded as vectors and vectors are sometimes made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the present paper, the results are organized in the following ways. First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this problem that arises in multistatic antenna array processing problem. Second, we extend the use of connection between the Hadamard (Kronecker) product and diagonal extraction (vector) operator in order to construct a computationally-efficient solution of non-homogeneous coupled matrix differential equations that useful in various applications. Finally, the analysis indicates that the Kronecker (Khatri-Rao) structure method can achieve good efficient while the Hadamard structure method achieve more efficient when the unknown matrices are diagonal.