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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Bibliographic Details
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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Summary:	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.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.2024289