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.
Citation: Na Li, Qin Zhong. Smoothing algorithm for the maximal eigenvalue of non-defective positive matrices[J]. AIMS Mathematics, 2024, 9(3): 5925-5936. doi: 10.3934/math.2024289
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.
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Na Li, Qin Zhong. Smoothing algorithm for the maximal eigenvalue of non-defective positive matrices[J]. AIMS Mathematics, 2024, 9(3): 5925-5936. doi: 10.3934/math.2024289
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