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

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 mon...

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Published in:AIMS mathematics Vol. 9; no. 3; pp. 5925 - 5936
Main Authors: Li, Na, Zhong, Qin
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2024
Subjects:
lower bound
maximal eigenvalue
non-defective
positive matrix
upper bound
ISSN:2473-6988, 2473-6988
Online Access:Get full text
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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.
AbstractList 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.
Author Li, Na
Zhong, Qin
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  organization: School of Intelligence Technology, Geely University of China, Chengdu 641423, China
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  fullname: Zhong, Qin
  organization: Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China
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Cites_doi 10.1142/8323
10.1007/s11432-022-3538-4
10.1155/2021/7230661
10.1112/jlms/s1-27.2.253
10.1016/j.laa.2021.10.003
10.1215/S0012-7094-57-02434-1
10.1080/03081087.2022.2081310
10.1112/jlms/s1-25.4.265
10.1016/j.laa.2017.05.021
10.1016/S0024-3795(96)90008-7
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Snippet This paper introduced a smoothing algorithm for calculating the maximal eigenvalue of non-defective positive matrices. Two special matrices were constructed to...
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StartPage 5925
SubjectTerms lower bound
maximal eigenvalue
non-defective
positive matrix
upper bound
Title Smoothing algorithm for the maximal eigenvalue of non-defective positive matrices
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