In this paper we study the numerical factorization of matrix
valued functions in order to apply them in the numerical 
solution of differential algebraic equations
with time varying coefficients.
The main difficulty is to obtain smoothness of the factors and a numerically
accessible form of their derivatives. We show how this can be achieved
without numerical differentiation if the derivative of the given matrix 
valued function is known. These results are then applied in the numerical
solution of differential algebraic Riccati equations. For this a numerical
algorithm is given and its properties are demonstrated by a numerical example. . /@