The Rate of Convergence of GMRES on a Tridiagonal Toeplitz Linear System. II
نویسندگان
چکیده
This paper continues the recent work of the authors’ (Numer. Math., to appear) on the rate of convergence of GMRES for a tridiagonal Toeplitz linear system Ax = b. Much simpler formulas than the earlier ones for GMRES residuals when b is the first or the last column of the identity matrix are established, and these formulas allow us to confirm the rate of convergence that was conjectured but only partially proven earlier. Simpler and sharper bounds than earlier ones when all b’s entries, except its first and last ones, are zeros are also obtained.
منابع مشابه
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system
The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛX−1 and then separate the study of GMRES convergence behavior into optimizing the condition number of X and a polynomial minimization problem over A’s spectrum. This artifi...
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