In this paper, we develop, study and implement a restricted additive Schwarz (RAS) preconditioner for speedup of the solution of sparse linear systems on NVIDIA Tesla GPU. A
novel algorithm for constructing this preconditioner is proposed. This algorithm involves two
phases. In the first phase, the construction of the RAS preconditioner is transformed to an
incomplete-LU problem. In the second phase, a parallel triangular solver is developed and the
incomplete-LU problem is solved by this solver. Numerical experiments show that the speedup of
this preconditioner is sufficiently high.