A Parallel Algorithm for Block Tridiagonal Systems

A parallel algorithm, namely parallel block diagonal dominant (PBDD) algorithm, is proposed to solve block tridiagonal linear systems on multi-computers. This algorithm is based on divided-and-conquer idea of the PDD method. When the systems is strictly block diagonal dominant, the PBDD is highly parallel and provides approximate solutions that equals to the exact solutions within machine accuracy. The PBDD method has been implemented on a 64-node multi-computer. The analytic results match closely with the results measured from the numerical experiments.