A nearness matrix is given with two constraints-least square constraint and symmetric positive semidefinite structure. It discusses problems: (1) the set γ of symmetric positive semidefinite real n×n matrices K to minimize the Frobenius norm of KX-F,where X, F are given matrices and (2) the element K in γ to minimize the Frobenius norm of C - K for any estimate matrix C. The conditions that γ is nonempty are given. An explicit form of elements in γ is provided and an explicit expression of the minimizer K is derived.
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