Abstract: This paper focused on parallel iterative method with parameters for solving banded or block tridiagonal linear systems on distributed-memory cluster．By splitting the coefficient matrix and using parameters,we proposed a new algorithm and gave some convergence theories for some special coefficient matrices．Furthermore,we implemented the algorithm on HP rx2600cluster and compared it with multisplitting method,BSOR method and PEk inner iterative me-thod for different examples．The numerical experiments indicate that acceleration rates and efficiency of our algorithm are higher than the multi-splitting one．The algorithm saves computational time by allocating memory properly．As to Example 1,the acceleration rates and efficiency of our algorithm are better than the BSOR one slightly．And the results for Example 2are better than PEk inner iterative one significantly.

Key words: Linear systems,HP rx2600cluster,Parallel efficiency,Acceleration rates