Let be the set of all matrices, the set of all symmetric matrices in . For , denotes the Frobenius norm. The authors consider the following two problems. Problem 1. Given , , , find such that . Problem 2. If Problem 1 is consistent, then denote its solutions by . For given , find such that
The authors describe an iterative method that determines the solvability of Problem 1 automatically and in the case of solvability computes a solution in an a priori known finite number of steps. Furthermore, the solution to Problem 2 can be found by choosing a suitable initial iteration matrix. It can also be found as the least-norm solution to another equation . The paper is carefully written with detailed and convincing proofs. It also contains a numerical example.