Stochastic estimation method of eigenvalue density for nonlinear eigenvalue problem on the complex plane

Abstract

The performance of some nonlinear eigenvalue problem solvers can be increased by setting parameters that are based on rough estimates of the desired eigenvalues. In the present paper, we propose a stochastic method for estimating the eigenvalue density for nonlinear eigenvalue problems of analytic matrix functions. The proposed method uses unbiased estimation of the matrix traces and contour integrations. Its performance is evaluated through the numerical experiments.