(untitled) (Journal of Computational Mathematics, 1994)
This paper studies the following two problem: Problem Ⅰ. Given X,B∈R^n×m, find A∈P_s,n, such that AX=B, where P_s,n=A∈SR^n×n|x^T AX≥0，∀S^Tx=0 , for given S∈R^n×p_p. Problem Ⅱ. Given A^*∈R^n×n, find A∈S_E, such that ||A^*-A||=inf_A∈S_E||A^*-A|| where S_E denotes the solutions set of Problem Ⅰ. The necessary and sufficient conditions for the solvability of Problem Ⅰ, the expression of the general solution of Problem Ⅰ and the solution of Problem Ⅱ are given for two case. For the general case, the equivalent form of conditions for the solvability of Problem Ⅰ is given.