The optimal approximation solution associated with a nonnegative definite constraint matrix equation

摘要

It is studied to find a positive semidefinite(not necessarily symmetric) matrix A satisying equation AX=B for given X, B. The solvable conditions are given and a general expression of the solutions is provided. The problem to find the positive semidefinite matrix  which minimizes A∗-A in Frobenius norm is considered, where matrix A satisfies AX=B. Some numerical results are also reported.