A Highly Parallel Systolic Tridiagonal Solver

概要

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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 competes finding the solution in 10(N/p)+6_p+23 time units, where p is the number of partitions of the system.
社団法人電子情報通信学会の論文
1996-09-25