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
In this paper, two spectral representations of the multidimensional dyadic stationary series and their correlation functions are given,and the isomorphic space of the value space of the multidimensional dyadic station...In this paper, two spectral representations of the multidimensional dyadic stationary series and their correlation functions are given,and the isomorphic space of the value space of the multidimensional dyadic stationary series is constructed.展开更多
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.
文摘In this paper, two spectral representations of the multidimensional dyadic stationary series and their correlation functions are given,and the isomorphic space of the value space of the multidimensional dyadic stationary series is constructed.
