| 2 | THE SOLVABILITY CONDITIONS FOR THE INVERSE PROBLEM OF MATRICES POSITIVE SEMIDEFINITE ON A SUBSPACE显示文摘This paper studies the following two problems:Problem Ⅰ. Given X, B ∈ Rnxm, find A ∈ Ps,n, such that AX = B, where Ps, n = {A ∈ SRnxn|XTA>0,STX = 0, for given S ∈ R}.Problem Ⅱ. Given A* ∈ Rnxn, find A ∈ SE, such that ||A*-A|| = infA∈SE||A* -A|| where SE denotes the solution 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 cases. For the general case, the equivalent form of conditions for the solvability of Problem Ⅰ is given. | HU, XY ZHANG, L DU, WZ | 1994 | Journal of Computational Mathematics1994，12，1： | 2 |
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