In this paper, we study the approximation problem on the closed convex cone, and prove that there exists a unique solution of the approximation problem, then give the algorithm to compute the unique solution.
This paper considers the following two problems:Problem I： Give X, B∈R^n×m, find A∈SAR^n×n such that AX = B Where SAR^n×n is the set of all n×n symmetric and sub-anti-symmetric matrices. Problem Ⅱ: Give A^～∈R^n×n find A^∈ SE such that ‖A^～-A^‖= minA∈SE‖A^～-A‖ Where SE is the solution set of problem I, ‖·‖ is the Frobenius norm. The necessary and sufficient conditions are studied for the set SE to be nonempty set, the general form of SE is given. For problem II, the expression of the solutionis provided.
