The upper bound for GMRES on normal tridiagonal Toeplitz linear system

Abstract

The Generalized Minimal Residual method

(GMRES) is often used to solve a large and spars system Ax=b.

This paper establishes error bound for residuals of GMRES on

solving a normal tridiagonal Toeplitz linear system.

this problem has been studied previously by Li [R.-C. Li,

Convergence of CG and GMRES on a tridiagonal Toeplitz linear

system, BIT 47 (3) (2007) 577-599.], for two special right-hand

sides.  Also, Li and Zhang [R.-C. Li, W.

Zhang, The rate of convergence of GMRES on a tridiagonal Toeplitz

linear system, Numer . Math. 112 (2009) 267-293.] for

non-symmetric matrix $A$, presented upper bound for GMRES

residuals. But in this paper we establish the upper bound on

normal tridiagonal Toeplitz linear systems for another special right-hand

sides.