ABSTRACT: In the field of computational particle transport, iterative acceleration methods are of great importance in improving convergence speed and computational performance. Acceleration methods are key to current nuclear reactor analysis, reducing the computational cost of reactor core simulations. Acceleration methods usually employ a ``high-order/low-order'' approach to iteratively solve the transport equation. However, current state-of-the-art techniques (such as the Coarse Mesh Finite Difference (CMFD) method) have operational limitations (such as limits on the size of the spatial grid discretization) that can lead to reduced performance or numerical instability. Another standard high-order/low-order method is the Quasidiffusion (QD) method. This method, which uses Eddington factors to correct the low-order diffusion equation, does not have such operational constraints. However, the QD method has the disadvantage of providing an approximate solution of the discrete ordinates (SN) equations. In this dissertation, we present a new advantageous iterative acceleration algorithm for neutron transport that reformulates and improves upon the QD method. This new method is called the {\em Generalized Quasidiffusion} (GQD) method. The general idea of the GQD method is to modify the Eddington factors to (i) make the accelerated solution equal to the solution of the SN equations, and (ii) to preserve the numerical stability and speed displayed by the classical QD method. The new {\em consistent Eddington factors} are formulated by preserving the net neutron leakage out of each spatial cell, between the high-order and low-order systems of equations. The new factors are calculated by solving an extra diffusion problem as an intermediate step between the high-order and low-order systems. We present numerical GQD results for a series of fixed-source, planar-geometry, monoenergetic, and isotropically-scattering neutron transport problems. Our results confirm that the GQD method provides a solution that is equal to the SN solution. The convergence rate and stability of the GQD method were evaluated in a series of different test problems, all of which displayed remarkable stability and convergence speed. A Fourier stability analysis was also conducted, providing theoretical validation for the numerical results. However, in some problems, the stability of the GQD method displayed sensitivity to the procedure used to obtain the consistent Eddington factors. A suggested procedure was introduced, which eliminated this issue for the presented case studies. This dissertation sets the groundwork for the new, consistent, unconditionally stable, and rapidly-converging GQD acceleration method for neutron transport calculations. It provides a straightforward formulation that can be extended to higher dimensions and can be implemented in current core simulation software. It also allows for straightforward implementation in existing QD codes.