An extension of analytic solutions of a class of constrained matrix minimization problems.
Journal of Computational and Applied Mathematics(2020)
摘要
In this paper we consider an extension of analytic solutions of a class of constrained matrix minimization problems and propose analytic solutions of the following matrix minimization problem: minSkSkH=In,LkLkH=Im|det(cIm±∏k=1sAkSkBkLk)|
minSkSkH=In,LkLkH=Im|tr(cIm±∏k=1sAkSkBkLk)|,where Ak∈Cm×n,Bk∈Cn×m,c is a complex number, Im denotes m-order identity matrix, and det(⋅),tr(⋅) denote matrix determinant and trace function. The proposed results improve the corresponding existing ones in Xu et al. (2019). Numerical examples are provided to illustrate the efficiency of the proposed theoretical results.
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关键词
Constrained matrix minimization problems,Singular value,Determinant/trace function
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