A highly parallel systolic tridiagonal solver

Many numerical simulation problems of natural phenomena are formulated by large tridiagonal and block tridiagonal linear systems. In this paper, an efficient parallel algorithm to solve a tridiagonal linear system is proposed. The algorithm named bi-recurrence algorithm has an inherent parallelism which is suitable for parallel processing. Its time complexity is 8N-4 for a tridiagonal linear system of order N. The complexity is little more than the Gaussian elimination algorithm. For parallel implementation with two processors, the time complexity is 4N-1. Based on the bi-recurrence algorithm, a VLSI oriented tridiagonal solver is designed, which has an architecture of 1-D linear systolic array with three processing cells. The systolic tridiagonal solver completes finding the solution of a tridiagonal linear system in 3N+6 units of time. A highly parallel systolic tridiagonal solver is also presented. The solver is characterized by highly parallel computability which originates in the divide-and-conquer strategy and high cost performance which originates in the systolic architecture. This solver completes finding the solution in 10(N/p) + 6p + 23 time units, where p is the number of partitions of the system.