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

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  • Singh, Sarishti
  • Panda, Geetanjali

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.

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  • Singh, Sarishti & Panda, Geetanjali, 2025. "Eigenvalue bounds and Perron-Frobenius theory for nonnegative or positive interval matrices," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    • Handle: RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000566
    DOI: 10.1016/j.amc.2025.129329
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    References listed on IDEAS

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    1. Hartman, David & Hladík, Milan & Říha, David, 2021. "Computing the spectral decomposition of interval matrices and a study on interval matrix powers," Applied Mathematics and Computation, Elsevier, vol. 403(C).
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