Vectorization of residual stop test for SOR methods

The iteration residuals are often used for a stop criterion in iterative methods for solution of linear systems. The computational costs of residual are likely expensive and nonnegligible. We propose in this article a vector form of residual computation for SOR iterative methods. The way we used is recombine the operations in SOR, so that a stop test related to residuals can be computed by a vector adding of parallelism, saving the matrix-by-vector multiplication required in the define of residual. The results of applying our approach to an instant are presented.