By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = D under the restriction that the solution matrix ...By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = D under the restriction that the solution matrix ∈ Rn×n is bisymmetric, where A ∈Rn×m and D ∈Rm×m are given matrices.展开更多
In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetri...In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A*-ALS||=inf||A*-A|| where SE is the solution set of problem Ｉ. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.展开更多
文摘By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = D under the restriction that the solution matrix ∈ Rn×n is bisymmetric, where A ∈Rn×m and D ∈Rm×m are given matrices.
文摘In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A*-ALS||=inf||A*-A|| where SE is the solution set of problem Ｉ. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.
