Convergence of CG and GMRES on a tridiagonal Toeplitz linear system

The Conjugate Gradient method (CG), the Minimal Residual method (MINRES), or more generally, the Generalized Minimal Residual method (GMRES) are widely used to solve a linear system Ax=b. The choice of a method depends on A’s symmetry property and/or definiteness), and MINRES is really just a special case of GMRES. This paper establishes error bounds on and sometimes exact expressions for residuals of CG, MINRES, and GMRES on solving a tridiagonal Toeplitz linear system, where A is Hermitian or just normal. These expressions and bounds are in terms of the three parameters that define A and Chebyshev polynomials of the first or second kind. AMS subject classification (2000)  65F10, 65N22