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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):799–803] and Li et al [Appl Math Comput 173 (2006):977–984] in certain cases.

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

Received 9 Feb 2021, Accepted 8 Aug 2021