A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

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.