Alireza Ataei

The method of the total least squares is one of the important problems in applied statistics and regression of error variables. In many applied problems, the observation variables also have errors. Considering the device Ax ≈ b in which the observation matrix A and the right-hand vector b have errors with using the method of the total least square and targeting the error in the matrix A and the right vector b, the approximate solution to the above problem will be calculated. On the other hand, due to the nonlinearity of the problem, the Gauss-Newton iteration method will be used. In the exact calculations of this method, through the analysis of the Single (A|b) solution of the problem of the total least square will be calculated. In this thesis, by using the iterative Gauss-Newton method, the problem of the total least square will be investigated and at the end, numerical results for the efficiency of this method presented.