Modified Newton method for the algebraic matrix Riccati equation part 3: Accelerating convergence

In the first two parts of this paper the practical usefulness of an algorit hm for solving algebraic matrix Riccati equations is demonstrated. The algo rithm uses Newton's method together with an infinite series solution for th e 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 equa tion to the total least squares problem is also considered and some illustr ative numerical examples are given.