# MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures

## TL;DR

The paper introduces MIXANDMIX, a numerical tool for efficiently computing empirical spectral distributions of random matrices from mixture models, featuring advanced algorithms and parallel computing for improved performance.

## Contribution

It presents novel numerical techniques including accelerated fixed point convergence, homotopy continuation, and non-uniform grid construction for spectral distribution computation.

## Key findings

- Competitive performance against existing packages
- Enhanced flexibility for mixture models
- Effective distribution support detection

## Abstract

The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the population distributions and the limiting spectral distribution can be obtained by solving a set of systems of non-linear equations, for which an efficient implementation is provided. The contributions include 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 approximation, 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.