THE UPPER BOUND FOR GMRES ON A TRIDIAGONAL TOEPLITZ LINEAR SYSTEM

The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric system Ax = b. This paper establishes error bound for residuals of GMRES on solving an N £ N tridiagonal Toeplitz linear system. This problem has been studied previously by Ren-Cang Li and Wei Zhang [2, 3]. But at this paper we establish the smaller error bound for special right-hand sides b = b(l)el (el is l-th column of Identity matrix), rather than [2, 3] as l ! N. Moreover, our proofs are simpler and smaller.