TY - JOUR
T1 - A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems
AU - Ze-Jia Xie, Xiao-Qing Jin & Zhi Zhao
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 827
EP - 836
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.181016.300517h
UR - https://global-sci.org/intro/article_detail/eajam/10723.html
KW - MINRES, Convergence bound, Hermitian indefinite, Toeplitz system.
AB - <p style="text-align: justify;">Some convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.</p>