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| 概要 |
A matrix with non-negative entries has a special eigenvalue, the so called Perron-Frobenius eigenvalue, which plays an important role in several fields of science [1]. In this paper we present a numer...ical tool to compute rigorous upper and lower bounds for the Perron-Frobenius eigenvalue of non-negative matrices. The idea is to express a non-negative matrix in terms of a directed graph, and make use of R. Tarjan’s algorithm [5] which finds all strongly connected components of a directed graph very efficiently. This enables us to decompose the original matrix into irreducible components (possibly of small size), and then to enclose the aimed Perron-Frobenius eigenvalue. We also show a numerical example which demonstrates the efficiency of our tool.続きを見る
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