Perturbation bounds for spectral radius and singular values of real nonnegative diagonally dominant tridiagonal matrix

Jiangjiang Li; Tianhua Liu

doi:10.1117/12.2648997

27 September 2022 Perturbation bounds for spectral radius and singular values of real nonnegative diagonally dominant tridiagonal matrix

Jiangjiang Li, Tianhua Liu

Author Affiliations +

Proceedings Volume 12345, International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022); 1234508 (2022) https://doi.org/10.1117/12.2648997
Event: 2022 International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 2022, Qingdao, China

Abstract

In this paper, we apply the perturbation theory on spectral radius and singular value of nonnegative diagonally dominant tridiagonal real matrix. It is found that if the off-diagonal elements and diagonally dominant vectors are bounded and form an inequality, then its spectral radius and singular value can be calculated with prescribed accuracies. In addition, our results can be applied to the problem of generalized eigenvalues.

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Jiangjiang Li and Tianhua Liu "Perturbation bounds for spectral radius and singular values of real nonnegative diagonally dominant tridiagonal matrix", Proc. SPIE 12345, International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 1234508 (27 September 2022); https://doi.org/10.1117/12.2648997

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