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Volume 47 Number 5 Volume 47 Number 6 Volume 48 Number 1

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Research articles

ScienceAsia 47 (2021): 773-778 |doi: 10.2306/scienceasia1513-1874.2021.092

Some new upper bounds for moduli of eigenvalues of iterative matrices

Jun He*, Yanmin Liu, Guangjun Xu

ABSTRACT:     Based on the matrix splitting M = P − Q, some upper bounds for the maximum of moduli of eigenvalues of the iteration matrix P−1Q are obtained when P is an strictly diagonally dominant (SDD) matrix or a doubly strictly diagonally dominant (DSDD) matrix. In this paper, some new upper bounds are introduced, which is applicable to a Dashnic-Zusmanovich (DZ) matrix P, and proved to be better than those in Huang and Gao [Int J Comput Math 80 (2003):799803] and Li et al [Appl Math Comput 173 (2006):977984] in certain cases.

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a School of mathematics, Zunyi Normal College, Zunyi, Guizhou, 563006 China

* Corresponding author, E-mail: hejunfan1@163.com

Received 9 Feb 2021, Accepted 8 Aug 2021