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Research Article | Open Access

Smoothing algorithm for the maximal eigenvalue of non-defective positive matrices

Na Li1, Qin Zhong2( )
School of Intelligence Technology, Geely University of China, Chengdu 641423, China
Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China
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Abstract

This paper introduced a smoothing algorithm for calculating the maximal eigenvalue of non-defective positive matrices. Two special matrices were constructed to provide monotonically increasing lower-bound estimates and monotonically decreasing upper-bound estimates of the maximal eigenvalue. The monotonicity and convergence of these estimations was also proven. Finally, the effectiveness of the algorithm was demonstrated with numerical examples.

Keywords

non-defectivepositive matrixmaximal eigenvalueupper boundlower bound
CLC number: 15A42, 15A18

References

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 5925-5936
DOI: 10.3934/math.2024289

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Cite this article:
Li N, Zhong Q. Smoothing algorithm for the maximal eigenvalue of non-defective positive matrices. AIMS Mathematics, 2024, 9(3): 5925-5936. https://doi.org/10.3934/math.2024289

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Received: 26 October 2023
Revised: 11 December 2023
Accepted: 10 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)