Eigenproblems in addition-min algebra

Meng Li; Xue-ping Wang

doi:10.3233/jifs-234499

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arXiv · 2302.08786

Eigenproblems in addition-min algebra

Meng Li·Xue-ping Wang

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Abstract

In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First, it provides a sufficient and necessary condition for a vector being an eigenvector of a given matrix, and then presents an algorithm for finding all eigenvalues and eigenvectors of a given matrix. It further proposes a sufficient and necessary condition for a vector being a constrained eigenvector of a given matrix and supplies an algorithm for computing all the constrained eigenvectors and eigenvalues of a given matrix. This article finally discusses the supereigenproblem of a given matrix and presents an algorithm for obtaining the maximum constrained supereigenvalue and depicting the feasible region of all the constrained supereigenvectors for a given matrix. It also gives some examples for illustrating the algorithms, respectively.

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BibTeX RIS

Meng Li, Xue-ping Wang. 2023-02-17. Eigenproblems in addition-min algebra. https://doi.org/10.3233/jifs-234499

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