Optimized cyclic reduction for the solution of linear tridiagonal systems on parallel computers

Abstract

A parallel version of the cyclic reduction algorithm for the solution of tridiagonal linear systems is presented. The original problem is divided into subproblems which may be solved almost independently. Synchronizations among the processors involved is only needed to solve a reduced tridiagonal system whose dimension depends on the number of processors. Numerical tests have been performed on a linear array of processors. The obtained speedups show that this is the best possible parallel implementation of the cyclic reduction and one of the fastest algorithms for the solution of tridiagonal systems on a parallel computer with medium grain parallelism.