Abstract: The work presented in this paper focused on alternating-direction parallel iterative method for solving banded-linear systems on distributed-memory multi-computers. Firstly, the matrix was splitted by using the feature of the coefficient matrix, thus the communication only need twice between the adjacent processors per iteration step. Furthermore, the sufficient conditions for convergence were given when the coefficient matrix A is a Hermite positive definite matrix or Mmatrix respectively. Finally, the numerical experiments implemented on HP rx2600 cluster indicate that the algorithm's parallel acceleration rates and efficiency are higher than the multi-splitting method's.

Key words: Banded linear systems, Alternating-direction iteration, HP rx2600 cluster, Parallelism