This work investigates the solution of the multigroup neutron transport equation with a discrete ordinates method. More specifically, it focuses on the k-eigenvalue problem of the equation. In this case, the variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method [2] which has been applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, these are often compared to the unaccelerated power iteration method. Hence, the goal of this paper is to apply the Anderson acceleration method to the power iteration method, and compare its performance to the Chebyshev acceleration method.