Research on the Parallel Solving for Tri-diagonal Linear Systems

This paper introduces two methods for the solution of tridiagonal systems: exchange algorithm (the forth and back method) and parallel algorithm (partition method). We compare the solving process and complexity of the two types of algorithms, especially the communication complexity and computational complexity. We analyze the main facts of the efficiencies of partition method and double partition method. In conclusion, we sum up the deficiencies and shortcomings of the forth and back method and partition method, and put forward a new useful parallel algorithm which is simple and practical.