An inexact inverse iteration for computing the smallesteigenvalue of an irreducible $M$-matrix.
In this talk, we present an inexact inverse iteration method to find the minimal eigenvalueand the associated eigenvector of an irreducible $M$-matrix. We propose two different relaxation strategies for solving thelinear system of inner iterations. For theconvergence of these two iterations, we show they are globally linear and superlinear, respectively. Numerical examples are provided to illustrate the convergence of theory.