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The key issues in the design of a cross-layer optimization scheme for multiuser orthogonal frequency multiple access (OFDMA) systems are the optimal subcarrier, bit and rate distribution policies. In many recent researches, these allocation strategies are derived either through dynamic programming or via mathematical analysis. When the latter option is available, an additional iterative process is needed for the final solution to be obtained. This paper includes performance comparisons between the analytical and the numerical techniques as well as assessments on which of the existing iterative methods exhibits the highest effectiveness. Deductively, relying on system's evaluations, the semi-implicit root (SIR) mechanism produces the highest rapidity, precision and stability, in terms of convergence rate, root's accuracy and number of iterations.