Convergence rate of GMRES on tridiagonal block Toeplitz linear systems

摘要

Iterative methods such as generalized minimal residual (GMRES) method are used to solve large sparse linear systems. This paper is considered the GMRES method for solving N x N tridiagonal block Toeplitz linear systemsAx = b with m xm diagonal blocks, and establishes upper bounds for GMRES residuals. The coefficient matrix A becomes an m- tridiagonal Toeplitz matrix, and tridiagonal toeplitz systems are subcases of these systems. Also, we show that the GMRES method on mN x mN linear system Ax = b computes the exact solution in at most N steps.