A Monte Carlo approach to estimating the spectrum of large positive semidefinite matrices.

Abstract

The method presented in this paper aims at furnishing a series of numerical values to approximate the matrix eigenvalues. The method is based on a statistical model that involves the first three central moments of the eigenvalue distribution, and it relies on the solution of a nonlinear system of equations that implements the moment-matching method and on a subsequent procedure of Monte Carlo simulations. The method is only applicable to real positive semidefinite matrices (PSD), and it is especially useful when other techniques lead to computational problems, e.g., when the matrices become too large to be processed or the required storage space sets heavy limits to the computational process.