An algorithm for computing minimal Gergorin sets

The existing algorithms for computing the minimal Gergorin set are designed for small and medium size (irreducible) matrices and based on Perron root computations coupled with bisection method and sampling techniques. Here, we first discuss the drawbacks of the existing methods and present a new approach based on the modified Newton's method to find zeros of the parameter dependent left-most eigenvalue of a Z-matrix and a special curve tracing procedure. The advantages of the new approach are presented on several test examples that arise in practical applications. Copyright (c) 2015 John Wiley & Sons, Ltd.