A Parallel Solver for Diagonally Dominant Tridiagonal Linear Systems With Constant Synchronization Requirements

We propose a parallel solver which only requires one synchronization for diagonally dominant tridiagonal linear systems of equations. The amount of data transmitted in the only one communication round is related to the number of processors and independent of problem size (n). The parallel solver only needs about 23n float operations and one communication synchronization totally. The computation procedure can be dived into two parts: one we called pretreatment needs about 13n float operations and the other one we called kernel solver needs about I On float operations. In addition to showing its theoretical complexity, we have implemented this algorithm on a real distributed memory parallel machine. The results are very promising and show an almost linear speedup for large n indicating the efficiency and scalability of the proposed solver. In theory it can be used to solve arbitrary diagonally dominant tridiagonal linear systems correctly and efficiently.