We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + L X − 1 L T , where Q is symmetric positive definite and L is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE). We discuss how to use the butterfly S Z algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.