Convergence of Cg and Gmres on a Tridiagonal Toeplitz Linear System
نویسندگان
چکیده
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.
منابع مشابه
The Rate of Convergence of GMRES on a Tridiagonal Toeplitz Linear System. II
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