Calculating eigenvectors in max-algebra by mutation-sunflower method

TL;DR

This paper introduces the mutation-sunflower method, a new approach for calculating max-eigenvectors of nonnegative irreducible matrices, especially effective for sparse matrices, by solving simplified max-eigenproblems.

Contribution

The paper presents a novel mutation-sunflower method for max-eigenvector computation applicable to general irreducible matrices, with particular efficiency for sparse matrices.

Findings

Effective for sparse matrices

Reduces to solving simple max-eigenproblems

Includes instructive examples

Abstract

In this article we introduce a new method, which we call a mutation-sunflower method, for calculating max-eigenvectors of a nonnegative irreducible $n\times n$ matrix $A$. Our method works in the general irreducible case, but it is in comparison with existing methods most effective for some special classes of matrices for example for sparse enough matrices. Our method reduces to solving max-eigenproblems for simple mutation-sunflower matrices that have exactly one positive entry in each row. We include some instructive examples.