Abstract
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 tridiagonal block Toeplitz linear systems with diagonal blocks, and establishes upper bounds for GMRES residuals. The coefficient matrix becomes an m-tridiagonal Toeplitz matrix, and tridiagonal toeplitz systems are subcases of these systems. Also, we show that the GMRES method on linear system computes the exact solution in at most N steps.
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