Total Least Squares Solutions Of Inverse Problems For Matrices

The inverse problems of matrices have been widely used in control theory, vibration theory, structure design and so on. In practical applications, there are errors in the measured data, which don't ensure the solvability of the problems. The least squares solutions of inverse problems have been considered. However, the least squares approach has an underlying assumption that all the errors are confined to the right-hand side and this assumption is frequently unrealistic. So the total least squares solutions of inverse problems for matrices are discussed.The paper is concerned with the total least squares solutions of inverse problems AX = B. The general form of solution for the non symmetric matrix A is given, the expression of optimal approximation solution is presented, and an algorithm for solving the problem is described. The total least squares problem with symmetric and bisymmetry constraints is discussed respectively. A sufficient condition for existence of solution is derived by use of the theory of matrix Ricaati equation. The general form of solution is given if the problem has a solution, and the expression of optimal approximation solution is presented. Some numerical examples are given.