The upper bound for GMRES on normal tridiagonal Toeplitz linear system

Authors

  • Reza Doostaki Department of Mathematics, Islamic Azad University, Kahnooj Branch, Kerman, Iran
  • Andishe Hadian
  • Sedighe Azizi

DOI:

https://doi.org/10.30495/jme.v9i0.321

Keywords:

GMRES, Tridiagonal Toeplitz matrix, 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.

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Published

2015-08-19

Issue

Vol. 9

Section

Vol. 9, No. 3, (2015)

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