In the first two parts of this paper the practical usefulness of an algorithm for solving algebraic matrix Riccati equations is demonstrated. The algorithm uses Newton＇s method together with an infinite series solution for the associated linear matrix equations. In this third section of the paper a modified Newton method, which incorporates a line search and addition of a multiple of the identity matrix to the Jacobian, is proposed and its effect on convergence is investigated. The application of the matrix Riccati equation to the total least squares problem is also considered and some illustrative numerical examples are given.