Eigenvalue bounds and Perron-Frobenius theory for nonnegative or positive interval matrices

Sarishti Singh and Geetanjali Panda

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: This paper introduces two classes of regular interval matrices and establishes intervals that either include or exclude the real eigenvalues of positive interval matrices. The Perron-Frobenius theory is extended to the generalized interval eigenvalue problem for nonnegative interval matrices under certain conditions. Moreover, necessary and sufficient conditions are derived for the existence of a real scalar and a positive vector that satisfy the generalized interval eigenvalue problem for nonnegative interval matrices under certain conditions.

Keywords: Eigenvalue bounds; Interval matrix; Irreducible interval matrix; Perron-Frobenius theory (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000566

DOI: 10.1016/j.amc.2025.129329

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