Numerical techniques for the computation of sample spectral distributions of population mixtures
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This note describes some techniques developed for the computation of the sample eigenvalue distribution of random matrices generated by mixtures of populations. Within this model the mapping between the population distributions and the asymptotic sample distribution can be obtained by solving a set of systems of non-linear equations, for which we provide an efficient implementation. This work contributes by describing a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to non-admissible solutions, a blind non-uniform grid construction for effective distribution support detection and improved approximation at its edges, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.
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