Algorithms for Computing Bases for the Perron Eigenspace with Prescribed Nonnegativity and Combinatorial Properties
Michael Neumann, Hans Schneider · SIAM Journal on Matrix Analysis and Applications · 1994
Let P be an $n \times n$ nonnegative matrix. In this paper the authors introduce a method called the SCANBAS algorithm for computing a union of (Jordan) chains $\mathcal{C}$ corresponding to the Perron eigenvalue of P, such that $\mathcal{C}$ consists of nonnegative vectors only and such that at each height, $\mathcal{C}$ contains the maximal number of nonnegative vectors of that height possible in a height basis for the Perron eigenspace of P. It is further shown that $\mathcal{C}$ can be extended to a height basis for the Perron eigenspace of P. The chains are extracted from transform components of P that are, in turn, polynomials in P. When the Perron eigenspace has a Jordan basis consisting of nonnegative vectors only, this algorithm computes such a basis. The paper concludes with various examples computed by the algorithm using MATLAB. The work here continues and deepens work on computing nonnegative bases for the Perron eigenspace from polynomials in the matrix already begun by Hartwig, Neumann, and Rose and by Neumann and Schneider.