The linear-quadratic control model (LQCM) is very popular due to its applicability to many economic situations. An infinite-horizon equilibrium solution to such a model requires that we solve the algebraic matrix Riccati Equation. Numerical methods based on a modified Newton-Raphson iteration converge quadratically to this solution. We show that the computational complexity of each iteration can be substantially reduced from O(n 6 ) to O(n 4 ) by applying Broyden's method of rank-1 updates. This method achieves superlinear converges. Moreover, it maintains the generality of the original method in that it does not impose constraints on matrix structure.